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Theorem raltp 3427
 Description: Convert a quantification over a triple to a conjunction. (Contributed by NM, 13-Sep-2011.) (Revised by Mario Carneiro, 23-Apr-2015.)
Hypotheses
Ref Expression
raltp.1
raltp.2
raltp.3
raltp.4
raltp.5
raltp.6
Assertion
Ref Expression
raltp
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem raltp
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, 6raltpg 3423 . 2
81, 2, 3, 7mp3an 1232 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   w3a 885   wceq 1243   wcel 1393  wral 2306  cvv 2557  ctp 3377 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-sbc 2765  df-un 2922  df-sn 3381  df-pr 3382  df-tp 3383 This theorem is referenced by:  fztpval  8945
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