Theorem opeq1i 2486

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 2483	. 2 |- (A = B -> <.A, C>. = <.B, C>.)
3	1, 2	ax-mp 7	1 |- <.A, C>. = <.B, C>.

Syntax hints:   = wceq 954  <.cop 2407

This theorem is referenced by:  xpmapenlem2 4483  ltexpq 5060  halfpq 5062  axi2m1 5265  isumnn0nn 7150  geolim1i 7181  efseq0ex 7261  ef1tllem 7331  efm1lim 7359  indistps 7603  distps 7604

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-un 2046  df-sn 2408  df-pr 2409  df-op 2412

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