Theorem opeq1i 3822

Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)

Hypothesis

Ref	Expression
opeq1i.1	|- A = B

Assertion

Ref	Expression
opeq1i	|- <. A , C >. = <. B , C >.

Proof of Theorem opeq1i

Step	Hyp	Ref	Expression
1		opeq1i.1	. 2 |- A = B
2		opeq1 3819	. 2 |- ( A = B -> <. A , C >. = <. B , C >. )
3	1, 2	ax-mp 5	1 |- <. A , C >. = <. B , C >.

Syntax hints:   = wceq 1373   <.cop 3636

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642

This theorem is referenced by:  caucvgsrlemfv  7904  caucvgsr  7915  pitonnlem1  7958  axi2m1  7988  axcaucvg  8013  ennnfonelem1  12778  2strstr1g  12954  2strop1g  12956