Theorem difxp1 5437

Description: Difference law for Cartesian product. (Contributed by Scott Fenton, 18-Feb-2013.) (Revised by Mario Carneiro, 26-Jun-2014.)

Assertion

Ref	Expression
difxp1

Proof of Theorem difxp1

Step	Hyp	Ref	Expression
1		difxp 5436	. 2
2		difid 3896	. . . . 5
3	2	xpeq2i 5025	. . . 4
4		xp0 5430	. . . 4
5	3, 4	eqtri 2486	. . 3
6	5	uneq2i 3654	. 2
7		un0 3810	. 2
8	1, 6, 7	3eqtrri 2491	1

Syntax hints:  =wceq 1395  \cdif 3472  u.cun 3473  c0 3784  X.cxp 5002

This theorem is referenced by:  dfsup3OLD  7924  sxbrsigalem2  28257

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  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  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012