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Theorem 2pm13.193 28318
 Description: pm13.193 27611 for two variables. pm13.193 27611 is Theorem *13.193 in [WhiteheadRussell] p. 179. Derived from 2pm13.193VD 28679. (Contributed by Alan Sare, 8-Feb-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
2pm13.193

Proof of Theorem 2pm13.193
StepHypRef Expression
1 simpll 730 . . 3
2 simplr 731 . . 3
3 simpr 447 . . . . 5
4 sbequ2 1631 . . . . 5
51, 3, 4sylc 56 . . . 4
6 sbequ2 1631 . . . 4
72, 5, 6sylc 56 . . 3
81, 2, 7jca31 520 . 2
9 simpll 730 . . 3
10 simplr 731 . . 3
11 simpr 447 . . . . 5
12 sbequ1 1859 . . . . 5
1310, 11, 12sylc 56 . . . 4
14 sbequ1 1859 . . . 4
159, 13, 14sylc 56 . . 3
169, 10, 15jca31 520 . 2
178, 16impbii 180 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wsb 1629 This theorem is referenced by:  2sb5nd  28326  2sb5ndVD  28686  2sb5ndALT  28709 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-sb 1630
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