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Theorem bnj1322 32373
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj1322 (𝐴 = 𝐵 → (𝐴𝐵) = 𝐴)

Proof of Theorem bnj1322
StepHypRef Expression
1 eqimss 3933 . 2 (𝐴 = 𝐵𝐴𝐵)
2 df-ss 3860 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
31, 2sylib 221 1 (𝐴 = 𝐵 → (𝐴𝐵) = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  cin 3842  wss 3843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3400  df-in 3850  df-ss 3860
This theorem is referenced by:  bnj1321  32578
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