Theorem xpeq12i 5026

Description: Equality inference for Cartesian product. (Contributed by FL, 31-Aug-2009.)

Hypotheses

Ref	Expression
xpeq12i.1
xpeq12i.2

Assertion

Ref	Expression
xpeq12i

Proof of Theorem xpeq12i

Step	Hyp	Ref	Expression
1		xpeq12i.1	. 2
2		xpeq12i.2	. 2
3		xpeq12 5023	. 2
4	1, 2, 3	mp2an 672	1

Syntax hints:  =wceq 1395  X.cxp 5002

This theorem is referenced by:  xpssres  5313  imainrect  5453  cnvssrndm  5534  fpar  6904  canthwelem  9049  pjpm  18739  txbasval  20107  hausdiag  20146  ussval  20762  ex-xp  25157  ismgmOLD  25322  ghsubgolemOLD  25372  hh0oi  26822  idssxp  27469  fcnvgreu  27514  sitgclg  28284  isdrngo1  30359  trclubg  37785

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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-opab 4511  df-xp 5010