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Theorem r19.32r 2451
Description: One direction of Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers. For decidable propositions this is an equivalence. (Contributed by Jim Kingdon, 19-Aug-2018.)
Hypothesis
Ref Expression
r19.32r.1  F/
Assertion
Ref Expression
r19.32r

Proof of Theorem r19.32r
StepHypRef Expression
1 r19.32r.1 . . . 4  F/
2 orc 632 . . . . 5
32a1d 22 . . . 4
41, 3alrimi 1412 . . 3
5 df-ral 2305 . . . 4
6 olc 631 . . . . . 6
76imim2i 12 . . . . 5
87alimi 1341 . . . 4
95, 8sylbi 114 . . 3
104, 9jaoi 635 . 2
11 df-ral 2305 . 2
1210, 11sylibr 137 1
Colors of variables: wff set class
Syntax hints:   wi 4   wo 628  wal 1240   F/wnf 1346   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-gen 1335  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  r19.32vr  2452
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