Theorem opeq2i 2491

Description: Equality inference for ordered pairs.

Hypothesis

Ref	Expression
opeq1i.1	|- A = B

Assertion

Ref	Expression
opeq2i	|- <.C, A>. = <.C, B>.

Proof of Theorem opeq2i

Step	Hyp	Ref	Expression
1		opeq1i.1	. 2 |- A = B
2		opeq2 2488	. 2 |- (A = B -> <.C, A>. = <.C, B>.)
3	1, 2	ax-mp 7	1 |- <.C, A>. = <.C, B>.

Syntax hints:   = wceq 956  <.cop 2411

This theorem is referenced by:  fnressn 3837  fressnfv 3838  xpmapenlem2 4497  recmulpq 5070  addresr 5256  nvop 8305  phop 8477  avril1 8784

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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