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Theorem eqimssd 4029
Description: Equality implies inclusion, deduction version. (Contributed by SN, 6-Nov-2024.)
Hypothesis
Ref Expression
eqimssd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
eqimssd (𝜑𝐴𝐵)

Proof of Theorem eqimssd
StepHypRef Expression
1 eqimssd.1 . 2 (𝜑𝐴 = 𝐵)
2 ssid 3995 . 2 𝐵𝐵
31, 2eqsstrdi 4027 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wss 3939
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-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1774  df-cleq 2717  df-ss 3956
This theorem is referenced by:  eqimss  4031  fssrescdmd  7131  sraassab  21805  evls1maplmhm  22305  selvvvval  41883
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