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

Step	Hyp	Ref	Expression
1		r19.29af2OLD.2	. . 3
2		r19.29af2OLD.p	. . . 4
3		r19.29af2OLD.1	. . . . 5
4	3	exp31 604	. . . 4
5	2, 4	ralrimi 2857	. . 3
6	1, 5	jca 532	. 2
7		r19.29r 2993	. 2
8		r19.29af2OLD.c	. . 3
9		pm3.35 587	. . . 4
10	9	a1i 11	. . 3
11	8, 10	rexlimi 2939	. 2
12	6, 7, 11	3syl 20	1

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