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Theorem altopelaltxp 25786
 Description: Alternate ordered pair membership in a cross product. Note that, unlike opelxp 4900, there is no sethood requirement here. (Contributed by Scott Fenton, 22-Mar-2012.)
Assertion
Ref Expression
altopelaltxp

Proof of Theorem altopelaltxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elaltxp 25785 . 2
2 reeanv 2867 . . 3
3 eqcom 2437 . . . . 5
4 vex 2951 . . . . . 6
5 vex 2951 . . . . . 6
64, 5altopth 25779 . . . . 5
73, 6bitri 241 . . . 4
872rexbii 2724 . . 3
9 risset 2745 . . . 4
10 risset 2745 . . . 4
119, 10anbi12i 679 . . 3
122, 8, 113bitr4i 269 . 2
131, 12bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  wrex 2698  caltop 25766   caltxp 25767 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-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-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-altop 25768  df-altxp 25769
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