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Theorem pm2.21 153
 Description: A falsehood implies anything. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypothesis
Ref Expression
pm2.21.1
Assertion
Ref Expression
pm2.21

Proof of Theorem pm2.21
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 wfal 135 . . . 4
21id 25 . . 3
3 df-fal 127 . . . 4
41, 3a1i 28 . . 3
52, 4mpbi 82 . 2
6 wv 64 . . 3
7 pm2.21.1 . . 3
86, 7weqi 76 . . . 4
98id 25 . . 3
106, 7, 9cla4v 152 . 2
115, 10syl 16 1
 Colors of variables: type var term Syntax hints:  tv 1  hb 3  kc 5  kl 6   ke 7  kbr 9   wffMMJ2 11  wffMMJ2t 12  tfal 118  tal 122 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-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 This theorem is referenced by:  notval2  159  notnot  200  ax3  205
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