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Theorem scaid 17296

Description: Utility theorem: index-independent form of scalar df-sca 17249. (Contributed by Mario Carneiro, 19-Jun-2014.)

**Assertion**
Ref	Expression
scaid	⊢ Scalar = Slot (Scalar‘ndx)

**Proof of Theorem scaid**
Step	Hyp	Ref	Expression
1		df-sca 17249	. 2 ⊢ Scalar = Slot 5
2		5nn 12328	. 2 ⊢ 5 ∈ ℕ
3	1, 2	ndxid 17166	1 ⊢ Scalar = Slot (Scalar‘ndx)

Colors of variables: wff setvar class

Syntax hints: = wceq 1533 ‘cfv 6547 5c5 12300 Slot cslot 17150 ndxcnx 17162 Scalarcsca 17236

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5299 ax-nul 5306 ax-pow 5364 ax-pr 5428 ax-un 7739 ax-cnex 11194 ax-1cn 11196 ax-addcl 11198

This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2931 df-ral 3052 df-rex 3061 df-reu 3365 df-rab 3420 df-v 3465 df-sbc 3775 df-csb 3891 df-dif 3948 df-un 3950 df-in 3952 df-ss 3962 df-pss 3965 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-iun 4998 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6305 df-ord 6372 df-on 6373 df-lim 6374 df-suc 6375 df-iota 6499 df-fun 6549 df-fn 6550 df-f 6551 df-f1 6552 df-fo 6553 df-f1o 6554 df-fv 6555 df-ov 7420 df-om 7870 df-2nd 7993 df-frecs 8285 df-wrecs 8316 df-recs 8390 df-rdg 8429 df-nn 12243 df-2 12305 df-3 12306 df-4 12307 df-5 12308 df-slot 17151 df-ndx 17163 df-sca 17249

This theorem is referenced by: lmodsca 17309 ipssca 17321 resssca 17324 phlsca 17330 prdssca 17438 imassca 17501 mgpsca 20090 rmodislmod 20821 rmodislmodOLD 20822 srasca 21077 srascaOLD 21078 zlmsca 21461 psrsca 21903 opsrsca 22013 psr1sca2 22187 ply1sca2 22190 matsca 22352 matscaOLD 22353 tngsca 24595 resvsca 33118 bj-isrvec 36860 algsca 42687 mendsca 42695 mnringscad 43741

	
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