Theorem opeq1i 4220

Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)

Hypothesis

Ref	Expression
opeq1i.1

Assertion

Ref	Expression
opeq1i

Proof of Theorem opeq1i

Step	Hyp	Ref	Expression
1		opeq1i.1	. 2
2		opeq1 4217	. 2
3	1, 2	ax-mp 5	1

Syntax hints:  =wceq 1395  <.cop 4035

This theorem is referenced by:  axi2m1  9557  strlemor1  14724  grpbasex  14740  grpplusgx  14741  mat1dimelbas  18973  mat1dim0  18975  mat1dimid  18976  mat1dimscm  18977  mat1dimmul  18978  indistpsx  19511  mapfzcons  30648  uhgrepe  32378

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036