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Theorem difxp2 5269
 Description: Difference law for Cartesian product. (Contributed by Scott Fenton, 18-Feb-2013.) (Revised by Mario Carneiro, 26-Jun-2014.)
Assertion
Ref Expression
difxp2

Proof of Theorem difxp2
StepHypRef Expression
1 difxp 5267 . 2
2 difid 3747 . . . . 5
32xpeq1i 4859 . . . 4
4 0xp 4920 . . . 4
53, 4eqtri 2493 . . 3
65uneq1i 3575 . 2
7 uncom 3569 . . 3
8 un0 3762 . . 3
97, 8eqtri 2493 . 2
101, 6, 93eqtrri 2498 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   cdif 3387   cun 3388  c0 3722   cxp 4837 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455  df-xp 4845  df-rel 4846 This theorem is referenced by:  imadifxp  28288  sxbrsigalem2  29181
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