Theorem preq2i 3788

Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)

Hypothesis

Ref	Expression
preq1i.1	|- A = B

Assertion

Ref	Expression
preq2i	|- { C , A } = { C , B }

Proof of Theorem preq2i

Step	Hyp	Ref	Expression
1		preq1i.1	. 2 |- A = B
2		preq2 3785	. 2 |- ( A = B -> { C , A } = { C , B } )
3	1, 2	ax-mp 5	1 |- { C , A } = { C , B }

Syntax hints:   = wceq 1402   {cpr 3706

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-sn 3711  df-pr 3712

This theorem is referenced by:  opid  3917  funopg  5406  df2o2  6693  fzprval  10467  fz0to3un2pr  10508  fz0to4untppr  10509  fzo0to2pr  10614  fzo0to42pr  10616  2strstr1g  13453  setsvtx  16206