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Theorem rextp 3782
Description: Convert a quantification over a triple to a disjunction. (Contributed by Mario Carneiro, 23-Apr-2015.)
Hypotheses
Ref Expression
raltp.1
raltp.2
raltp.3
raltp.4
raltp.5
raltp.6
Assertion
Ref Expression
rextp
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rextp
StepHypRef Expression
1 raltp.1 . 2
2 raltp.2 . 2
3 raltp.3 . 2
4 raltp.4 . . 3
5 raltp.5 . . 3
6 raltp.6 . . 3
74, 5, 6rextpg 3778 . 2
81, 2, 3, 7mp3an 1277 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   w3o 933   wceq 1642   wcel 1710  wrex 2615  cvv 2859  ctp 3739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-tp 3743
This theorem is referenced by: (None)
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