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Theorem bnj1262 32156
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1262.1 𝐴𝐵
bnj1262.2 (𝜑𝐶 = 𝐴)
Assertion
Ref Expression
bnj1262 (𝜑𝐶𝐵)

Proof of Theorem bnj1262
StepHypRef Expression
1 bnj1262.2 . 2 (𝜑𝐶 = 𝐴)
2 bnj1262.1 . 2 𝐴𝐵
31, 2eqsstrdi 3996 1 (𝜑𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538  wss 3908
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-in 3915  df-ss 3925
This theorem is referenced by:  bnj229  32230  bnj1128  32336  bnj1145  32339
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