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Theorem r19.29af2OLD 2996
 Description: A commonly used pattern based on r19.29 2992. (Contributed by Thierry Arnoux, 17-Dec-2017.) Obsolete version of r19.29af2 2995 as of 25-Mar-2020. (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
r19.29af2OLD.p
r19.29af2OLD.c
r19.29af2OLD.1
r19.29af2OLD.2
Assertion
Ref Expression
r19.29af2OLD

Proof of Theorem r19.29af2OLD
StepHypRef Expression
1 r19.29af2OLD.2 . . 3
2 r19.29af2OLD.p . . . 4
3 r19.29af2OLD.1 . . . . 5
43exp31 604 . . . 4
52, 4ralrimi 2857 . . 3
61, 5jca 532 . 2
7 r19.29r 2993 . 2
8 r19.29af2OLD.c . . 3
9 pm3.35 587 . . . 4
109a1i 11 . . 3
118, 10rexlimi 2939 . 2
126, 7, 113syl 20 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  F/wnf 1616  e.wcel 1818  A.wral 2807  E.wrex 2808 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813
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