Theorem nfmov 2549

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2551 for a version without disjoint variable conditions but requiring ax-13 2366. (Contributed by NM, 9-Mar-1995.) (Revised by Wolf Lammen, 2-Oct-2023.)

Hypothesis

Ref	Expression
nfmov.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfmov	⊢ Ⅎ𝑥∃*𝑦𝜑

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfmov

Step	Hyp	Ref	Expression
1		nftru 1799	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2548	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1541	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1535  Ⅎwnf 1778  ∃*wmo 2527

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-11 2147  ax-12 2164

This theorem depends on definitions:  df-bi 206  df-or 847  df-tru 1537  df-ex 1775  df-nf 1779  df-mo 2529

This theorem is referenced by:  mo3  2553  2moexv  2618  moexexvw  2619  2moswapv  2620  2euexv  2622  2mo  2639  nfrmow  3404  reusv1  5391  reusv2lem1  5392  mosubopt  5506  dffun6f  6560

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