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Theorem rextp 3419
Description: Convert a quantification over a triple to a disjunction. (Contributed by Mario Carneiro, 23-Apr-2015.)
Hypotheses
Ref Expression
raltp.1  _V
raltp.2  _V
raltp.3  C 
_V
raltp.4
raltp.5
raltp.6  C
Assertion
Ref Expression
rextp  { ,  ,  C }
Distinct variable groups:   ,   ,   , C   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rextp
StepHypRef Expression
1 raltp.1 . 2  _V
2 raltp.2 . 2  _V
3 raltp.3 . 2  C 
_V
4 raltp.4 . . 3
5 raltp.5 . . 3
6 raltp.6 . . 3  C
74, 5, 6rextpg 3415 . 2  _V  _V  C  _V  { ,  ,  C }
81, 2, 3, 7mp3an 1231 1  { ,  ,  C }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   w3o 883   wceq 1242   wcel 1390  wrex 2301   _Vcvv 2551   {ctp 3369
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3or 885  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-sn 3373  df-pr 3374  df-tp 3375
This theorem is referenced by: (None)
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