Theorem r19.29af2 2995

Description: A commonly used pattern based on r19.29 2992. (Contributed by Thierry Arnoux, 17-Dec-2017.) (Proof shortened by OpenAI, 25-Mar-2020.)

Hypotheses

Ref	Expression
r19.29af2.p
r19.29af2.c
r19.29af2.1
r19.29af2.2

Assertion

Ref	Expression
r19.29af2

Proof of Theorem r19.29af2

Step	Hyp	Ref	Expression
1		r19.29af2.2	. 2
2		r19.29af2.p	. . 3
3		r19.29af2.c	. . 3
4		r19.29af2.1	. . . 4
5	4	exp31 604	. . 3
6	2, 3, 5	rexlimd 2941	. 2
7	1, 6	mpd 15	1

Syntax hints:  ->wi 4  /\wa 369  F/wnf 1616  e.wcel 1818  E.wrex 2808

This theorem is referenced by:  r19.29af  2997  restmetu  21090  locfinreflem  27843

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