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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
StepHypRef Expression
1 r19.29af2.2 . 2
2 r19.29af2.p . . 3
3 r19.29af2.c . . 3
4 r19.29af2.1 . . . 4
54exp31 604 . . 3
62, 3, 5rexlimd 2941 . 2
71, 6mpd 15 1
 Colors of variables: wff setvar class 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
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