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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
StepHypRef Expression
1 difxp 5436 . 2
2 difid 3896 . . . . 5
32xpeq2i 5025 . . . 4
4 xp0 5430 . . . 4
53, 4eqtri 2486 . . 3
65uneq2i 3654 . 2
7 un0 3810 . 2
81, 6, 73eqtrri 2491 1
 Colors of variables: wff setvar class 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
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