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Theorem 2pm13.193 27011
 Description: pm13.193 26778 for two variables. pm13.193 26778 is Theorem *13.193 in [WhiteheadRussell] p. 179. Derived from 2pm13.193VD 27369. (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 733 . . 3
2 simplr 734 . . 3
3 simpr 449 . . . . 5
4 sbequ2 1890 . . . . 5
51, 3, 4sylc 58 . . . 4
6 sbequ2 1890 . . . 4
72, 5, 6sylc 58 . . 3
81, 2, 7jca31 522 . 2
9 simpll 733 . . 3
10 simplr 734 . . 3
11 simpr 449 . . . . 5
12 sbequ1 1889 . . . . 5
1310, 11, 12sylc 58 . . . 4
14 sbequ1 1889 . . . 4
159, 13, 14sylc 58 . . 3
169, 10, 15jca31 522 . 2
178, 16impbii 182 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wsb 1882 This theorem is referenced by:  2sb5nd  27019  2sb5ndVD  27376  2sb5ndALT  27399 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-sb 1883
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