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Theorem preq1i 4645
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 4642 . 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 1538  {cpr 4542
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2793
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2071  df-clab 2800  df-cleq 2814  df-clel 2892  df-v 3473  df-un 3915  df-sn 4541  df-pr 4543
This theorem is referenced by:  funopg  6362  frcond1  28030  n4cyclfrgr  28055  disjdifprg2  30313
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