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Theorem xpdom1g 7206
 Description: Dominance law for cross product. Theorem 6L(c) of [Enderton] p. 149. (Contributed by NM, 25-Mar-2006.) (Revised by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
xpdom1g

Proof of Theorem xpdom1g
StepHypRef Expression
1 reldom 7116 . . . 4
21brrelexi 4919 . . 3
3 xpcomeng 7201 . . . 4
43ancoms 441 . . 3
52, 4sylan2 462 . 2
6 xpdom2g 7205 . . 3
71brrelex2i 4920 . . . 4
8 xpcomeng 7201 . . . 4
97, 8sylan2 462 . . 3
10 domentr 7167 . . 3
116, 9, 10syl2anc 644 . 2
12 endomtr 7166 . 2
135, 11, 12syl2anc 644 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1726  cvv 2957   class class class wbr 4213   cxp 4877   cen 7107   cdom 7108 This theorem is referenced by:  xpdom1  7208  xpen  7271  infpwfien  7944  iunctb  8450  canthp1lem1  8528  gchxpidm  8545  xpct  24103  fnct  24106 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pow 4378  ax-pr 4404  ax-un 4702 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-csb 3253  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-pw 3802  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-mpt 4269  df-id 4499  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-rn 4890  df-res 4891  df-ima 4892  df-iota 5419  df-fun 5457  df-fn 5458  df-f 5459  df-f1 5460  df-fo 5461  df-f1o 5462  df-fv 5463  df-1st 6350  df-2nd 6351  df-en 7111  df-dom 7112
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