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Theorem bnj1322 29953
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 3619 . 2 (𝐴 = 𝐵𝐴𝐵)
2 df-ss 3553 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
31, 2sylib 206 1 (𝐴 = 𝐵 → (𝐴𝐵) = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1474  cin 3538  wss 3539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-in 3546  df-ss 3553
This theorem is referenced by:  bnj1321  30155
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