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Theorem r19.29af2 3005
 Description: A commonly used pattern based on r19.29 3002 (Contributed by Thierry Arnoux, 17-Dec-2017.)
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 . . 3
2 r19.29af2.p . . . 4
3 r19.29af2.1 . . . . 5
43exp31 604 . . . 4
52, 4ralrimi 2867 . . 3
61, 5jca 532 . 2
7 r19.29r 3003 . 2
8 r19.29af2.c . . 3
9 pm3.35 587 . . . 4
109a1i 11 . . 3
118, 10rexlimi 2949 . 2
126, 7, 113syl 20 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wnf 1599   wcel 1767  wral 2817  wrex 2818 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600  df-ral 2822  df-rex 2823 This theorem is referenced by:  r19.29af  3006  restmetu  20958  locfinreflem  27668
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