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Theorem raltp 3855
 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 3851 . 2
81, 2, 3, 7mp3an 1279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936   wceq 1652   wcel 1725  wral 2697  cvv 2948  ctp 3808 This theorem is referenced by:  fztpval  11097 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-sbc 3154  df-un 3317  df-sn 3812  df-pr 3813  df-tp 3814
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