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Theorem 19.12b 24229
 Description: 19.12vv 1851 with not-free hypotheses, instead of distinct variable conditions. (Contributed by Scott Fenton, 13-Dec-2010.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
19.12b.1
19.12b.2
Assertion
Ref Expression
19.12b
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem 19.12b
StepHypRef Expression
1 19.12b.1 . . . 4
2119.21 1803 . . 3
32exbii 1572 . 2
4 19.12b.2 . . . 4
54nfal 1778 . . 3
6519.36 1819 . 2
7419.36 1819 . . . 4
87albii 1556 . . 3
91nfal 1778 . . . 4
10919.21 1803 . . 3
118, 10bitr2i 241 . 2
123, 6, 113bitri 262 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530  wex 1531  wnf 1534 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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