Theorem opeq1i 2490

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 2487	. 2 |- (A = B -> <.A, C>. = <.B, C>.)
3	1, 2	ax-mp 7	1 |- <.A, C>. = <.B, C>.

Syntax hints:   = wceq 956  <.cop 2411

This theorem is referenced by:  xpmapenlem2 4497  ltexpq 5080  halfpq 5082  axi2m1 5285  isumnn0nn 7207  geolim1i 7238  efseq0ex 7311  ef1tllem 7381  efm1lim 7411  indistps 7653  distps 7654

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-sn 2412  df-pr 2413  df-op 2416

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