Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rextp Structured version   Unicode version

Theorem rextp 3866
 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 3862 . 2
81, 2, 3, 7mp3an 1280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3o 936   wceq 1653   wcel 1726  wrex 2708  cvv 2958  ctp 3818 This theorem is referenced by:  1cubr  20687 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-v 2960  df-sbc 3164  df-un 3327  df-sn 3822  df-pr 3823  df-tp 3824
 Copyright terms: Public domain W3C validator