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Theorem frinxp 4944
 Description: Intersection of well-founded relation with cross product of its field. (Contributed by Mario Carneiro, 10-Jul-2014.)
Assertion
Ref Expression
frinxp

Proof of Theorem frinxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 3343 . . . . . . . . . . 11
2 ssel 3343 . . . . . . . . . . 11
31, 2anim12d 548 . . . . . . . . . 10
4 brinxp 4941 . . . . . . . . . . 11
54ancoms 441 . . . . . . . . . 10
63, 5syl6 32 . . . . . . . . 9
76impl 605 . . . . . . . 8
87notbid 287 . . . . . . 7
98ralbidva 2722 . . . . . 6
109rexbidva 2723 . . . . 5
1110adantr 453 . . . 4
1211pm5.74i 238 . . 3
1312albii 1576 . 2
14 df-fr 4542 . 2
15 df-fr 4542 . 2
1613, 14, 153bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550   wcel 1726   wne 2600  wral 2706  wrex 2707   cin 3320   wss 3321  c0 3629   class class class wbr 4213   wfr 4539   cxp 4877 This theorem is referenced by:  weinxp  4946 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-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 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-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-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-br 4214  df-opab 4268  df-fr 4542  df-xp 4885
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