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Theorem con3d 162
 Description: A contraposition deduction. (Contributed by Mario Carneiro, 10-Oct-2014.)
Hypothesis
Ref Expression
con3d.1
Assertion
Ref Expression
con3d

Proof of Theorem con3d
StepHypRef Expression
1 wnot 138 . . 3
2 con3d.1 . . . 4
32ax-cb2 30 . . 3
41, 3wc 50 . 2
53notnot1 160 . . 3
62, 5syl 16 . 2
74, 6con2d 161 1
 Colors of variables: type var term Syntax hints:  hb 3  kc 5  kct 10   wffMMJ2 11   tne 120 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-distrl 70  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113 This theorem depends on definitions:  df-ov 73  df-al 126  df-fal 127  df-an 128  df-im 129  df-not 130 This theorem is referenced by:  alnex  186
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