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Theorem preq1i 4241
Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypothesis
Ref Expression
preq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
preq1i {𝐴, 𝐶} = {𝐵, 𝐶}

Proof of Theorem preq1i
StepHypRef Expression
1 preq1i.1 . 2 𝐴 = 𝐵
2 preq1 4238 . 2 (𝐴 = 𝐵 → {𝐴, 𝐶} = {𝐵, 𝐶})
31, 2ax-mp 5 1 {𝐴, 𝐶} = {𝐵, 𝐶}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  {cpr 4150
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-un 3560  df-sn 4149  df-pr 4151
This theorem is referenced by:  funopg  5880  frcond1  26996  n4cyclfrgr  27019  disjdifprg2  29231
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