Theorem preq2i 3491

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 3488	. 2 |- ( A = B -> { C , A } = { C , B } )
3	1, 2	ax-mp 7	1 |- { C , A } = { C , B }

Syntax hints:   = wceq 1285   {cpr 3417

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-sn 3422  df-pr 3423

This theorem is referenced by:  opid  3608  funopg  4984  df2o2  6099  fzprval  9227  fzo0to2pr  9356  fzo0to42pr  9358