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Theorem r19.29af2 2497
 Description: A commonly used pattern based on r19.29 2495 (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 356 . . . 4
52, 4ralrimi 2433 . . 3
61, 5jca 300 . 2
7 r19.29r 2496 . 2
8 r19.29af2.c . . 3
9 pm3.35 339 . . . 4
109a1i 9 . . 3
118, 10rexlimi 2471 . 2
126, 7, 113syl 17 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wnf 1390   wcel 1434  wral 2349  wrex 2350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-ral 2354  df-rex 2355 This theorem is referenced by:  r19.29af  2498
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