Theorem opeq2i 2495

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 2492	. 2 |- (A = B -> <.C, A>. = <.C, B>.)
3	1, 2	ax-mp 7	1 |- <.C, A>. = <.C, B>.

Syntax hints:   = wceq 958  <.cop 2415

This theorem is referenced by:  fnressn 3843  fressnfv 3844  xpmapenlem2 4503  recmulpq 5082  addresr 5268  nvop 8301  phop 8473  avril1 8779

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-sn 2416  df-pr 2417  df-op 2420

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