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Theorem preq1i 4736
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 4733 . 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 1540  {cpr 4628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-sn 4627  df-pr 4629
This theorem is referenced by:  funopg  6600  frcond1  30285  n4cyclfrgr  30310  disjdifprg2  32589
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