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Theorem bnj1322 34837
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 4041 . 2 (𝐴 = 𝐵𝐴𝐵)
2 dfss2 3968 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
31, 2sylib 218 1 (𝐴 = 𝐵 → (𝐴𝐵) = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539  cin 3949  wss 3950
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-in 3957  df-ss 3967
This theorem is referenced by:  bnj1321  35042
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