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Theorem distrc 93
 Description: Distribution of combination over substitution. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
distrc.1
distrc.2
distrc.3
Assertion
Ref Expression
distrc

Proof of Theorem distrc
StepHypRef Expression
1 weq 41 . 2
2 distrc.1 . . . . 5
3 distrc.2 . . . . 5
42, 3wc 50 . . . 4
54wl 66 . . 3
6 distrc.3 . . 3
75, 6wc 50 . 2
82wl 66 . . . 4
98, 6wc 50 . . 3
103wl 66 . . . 4
1110, 6wc 50 . . 3
129, 11wc 50 . 2
133, 6, 2ax-distrc 68 . 2
141, 7, 12, 13dfov2 75 1
 Colors of variables: type var term Syntax hints:   ht 2  kc 5  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51  ax-wl 65  ax-distrc 68  ax-wov 71 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  hbc  110
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