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Theorem bnj1262 31981
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 4018 1 (𝜑𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  wss 3933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-in 3940  df-ss 3949
This theorem is referenced by:  bnj229  32055  bnj1128  32159  bnj1145  32162
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