Theorem opeq1i 2544

Description: Equality inference for ordered pairs.

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 2541	. 2 |- (A = B -> <.A, C>. = <.B, C>.)
3	1, 2	ax-mp 7	1 |- <.A, C>. = <.B, C>.

Syntax hints:   = wceq 997  <.cop 2463

This theorem is referenced by:  xpmapenlem2 4562  ltexpq 5145  halfpq 5147  axi2m1 5350  isumnn0nn 7297  geolim1i 7328  efseq0ex 7401  ef1tllem 7471  efm1limi 7502  indistps 7738  distps 7739

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1003  ax-gen 1004  ax-8 1005  ax-10 1007  ax-12 1009  ax-17 1012  ax-4 1014  ax-5o 1016  ax-6o 1019  ax-9o 1164  ax-10o 1182  ax-16 1252  ax-11o 1260  ax-ext 1504

This theorem depends on definitions:  df-bi 154  df-or 231  df-an 232  df-ex 1022  df-sb 1214  df-clab 1510  df-cleq 1515  df-clel 1518  df-v 1859  df-un 2101  df-sn 2464  df-pr 2465  df-op 2468

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