Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reximd2a Structured version   Unicode version

Theorem reximd2a 2913
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by Thierry Arnoux, 27-Jan-2020.)
Hypotheses
Ref Expression
reximd2a.1
reximd2a.2
reximd2a.3
reximd2a.4
Assertion
Ref Expression
reximd2a

Proof of Theorem reximd2a
StepHypRef Expression
1 reximd2a.4 . 2
2 reximd2a.1 . . . 4
3 reximd2a.2 . . . . . 6
4 reximd2a.3 . . . . . 6
53, 4jca 532 . . . . 5
65expl 618 . . . 4
72, 6eximd 1868 . . 3
8 df-rex 2799 . . 3
9 df-rex 2799 . . 3
107, 8, 93imtr4g 270 . 2
111, 10mpd 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wex 1599  wnf 1603   wcel 1804  wrex 2794 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-12 1840 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1600  df-nf 1604  df-rex 2799 This theorem is referenced by:  locfinreflem  27821
 Copyright terms: Public domain W3C validator