Theorem preq2i 3724

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 3721	. 2 |- ( A = B -> { C , A } = { C , B } )
3	1, 2	ax-mp 5	1 |- { C , A } = { C , B }

Syntax hints:   = wceq 1373   {cpr 3644

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-sn 3649  df-pr 3650

This theorem is referenced by:  opid  3851  funopg  5324  df2o2  6540  fzprval  10239  fz0to3un2pr  10280  fz0to4untppr  10281  fzo0to2pr  10384  fzo0to42pr  10386  2strstr1g  13069