Theorem preq2i 3657

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 3654	. 2 |- ( A = B -> { C , A } = { C , B } )
3	1, 2	ax-mp 5	1 |- { C , A } = { C , B }

Syntax hints:   = wceq 1343   {cpr 3577

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583

This theorem is referenced by:  opid  3776  funopg  5222  df2o2  6399  fzprval  10017  fz0to3un2pr  10058  fz0to4untppr  10059  fzo0to2pr  10153  fzo0to42pr  10155  2strstr1g  12498