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Theorem poinxp 4941
 Description: Intersection of partial order with cross product of its field. (Contributed by Mario Carneiro, 10-Jul-2014.)
Assertion
Ref Expression
poinxp

Proof of Theorem poinxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simpll 731 . . . . . . . 8
2 brinxp 4940 . . . . . . . 8
31, 1, 2syl2anc 643 . . . . . . 7
43notbid 286 . . . . . 6
5 brinxp 4940 . . . . . . . . 9
65adantr 452 . . . . . . . 8
7 brinxp 4940 . . . . . . . . 9
87adantll 695 . . . . . . . 8
96, 8anbi12d 692 . . . . . . 7
10 brinxp 4940 . . . . . . . 8
1110adantlr 696 . . . . . . 7
129, 11imbi12d 312 . . . . . 6
134, 12anbi12d 692 . . . . 5
1413ralbidva 2721 . . . 4
1514ralbidva 2721 . . 3
1615ralbiia 2737 . 2
17 df-po 4503 . 2
18 df-po 4503 . 2
1916, 17, 183bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   wcel 1725  wral 2705   cin 3319   class class class wbr 4212   wpo 4501   cxp 4876 This theorem is referenced by:  soinxp  4942 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-po 4503  df-xp 4884
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