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Theorem preq1i 3687
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 3684 . 2 (𝐴 = 𝐵 → {𝐴, 𝐶} = {𝐵, 𝐶})
31, 2ax-mp 5 1 {𝐴, 𝐶} = {𝐵, 𝐶}
Colors of variables: wff set class
Syntax hints:   = wceq 1364  {cpr 3608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614
This theorem is referenced by:  funopg  5269
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