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Theorem seinxp 4936
 Description: Intersection of set-like relation with cross product of its field. (Contributed by Mario Carneiro, 22-Jun-2015.)
Assertion
Ref Expression
seinxp Se Se

Proof of Theorem seinxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 brinxp 4932 . . . . . 6
21ancoms 440 . . . . 5
32rabbidva 2939 . . . 4
43eleq1d 2501 . . 3
54ralbiia 2729 . 2
6 df-se 4534 . 2 Se
7 df-se 4534 . 2 Se
85, 6, 73bitr4i 269 1 Se Se
 Colors of variables: wff set class Syntax hints:   wb 177   wcel 1725  wral 2697  crab 2701  cvv 2948   cin 3311   class class class wbr 4204   Se wse 4531   cxp 4868 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-se 4534  df-xp 4876
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