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Theorem rextp 3456
 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 3452 . 2
81, 2, 3, 7mp3an 1243 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102   w3o 895   wceq 1259   wcel 1409  wrex 2324  cvv 2574  ctp 3405 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3or 897  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-sbc 2788  df-un 2950  df-sn 3409  df-pr 3410  df-tp 3411 This theorem is referenced by: (None)
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