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Theorem exopxfr2 6411
 Description: Transfer ordered-pair existence from/to single variable existence. (Contributed by NM, 26-Feb-2014.)
Hypothesis
Ref Expression
exopxfr2.1
Assertion
Ref Expression
exopxfr2
Distinct variable groups:   ,,,   ,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem exopxfr2
StepHypRef Expression
1 df-rel 4885 . . . . . . 7
21biimpi 187 . . . . . 6
32sseld 3347 . . . . 5
43adantrd 455 . . . 4
54pm4.71rd 617 . . 3
65rexbidv2 2728 . 2
7 eleq1 2496 . . . 4
8 exopxfr2.1 . . . 4
97, 8anbi12d 692 . . 3
109exopxfr 6410 . 2
116, 10syl6bb 253 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  wrex 2706  cvv 2956   wss 3320  cop 3817   cxp 4876   wrel 4883 This theorem is referenced by:  dvhopellsm  31915 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-sbc 3162  df-csb 3252  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-iun 4095  df-opab 4267  df-xp 4884  df-rel 4885
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