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Theorem el2xptp 6842
 Description: A member of a nested Cartesian product is an ordered triple. (Contributed by Alexander van der Vekens, 15-Feb-2018.)
Assertion
Ref Expression
el2xptp
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem el2xptp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elxp2 5026 . 2
2 opeq1 4219 . . . . 5
32eqeq2d 2471 . . . 4
43rexbidv 2968 . . 3
54rexxp 5155 . 2
6 df-ot 4041 . . . . . . 7
76eqcomi 2470 . . . . . 6
87eqeq2i 2475 . . . . 5
98rexbii 2959 . . . 4
109rexbii 2959 . . 3
1110rexbii 2959 . 2
121, 5, 113bitri 271 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1395   wcel 1819  wrex 2808  cop 4038  cotp 4040   cxp 5006 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3431  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-ot 4041  df-iun 4334  df-opab 4516  df-xp 5014  df-rel 5015 This theorem is referenced by:  2spotmdisj  25194
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