Theorem opeq1i 3672

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 3669	. 2 |- ( A = B -> <. A , C >. = <. B , C >. )
3	1, 2	ax-mp 7	1 |- <. A , C >. = <. B , C >.

Syntax hints:   = wceq 1312   <.cop 3494

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095

This theorem depends on definitions:  df-bi 116  df-3an 945  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-un 3039  df-sn 3497  df-pr 3498  df-op 3500

This theorem is referenced by:  caucvgsrlemfv  7527  caucvgsr  7538  pitonnlem1  7574  axi2m1  7604  axcaucvg  7629  ennnfonelem1  11759  2strstr1g  11899  2strop1g  11901