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Theorem ceq12 88
 Description: Equality theorem for combination. (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypotheses
Ref Expression
ceq12.1
ceq12.2
ceq12.3
ceq12.4
Assertion
Ref Expression
ceq12

Proof of Theorem ceq12
StepHypRef Expression
1 weq 41 . 2
2 ceq12.1 . . 3
3 ceq12.2 . . 3
42, 3wc 50 . 2
5 ceq12.3 . . . 4
62, 5eqtypi 78 . . 3
7 ceq12.4 . . . 4
83, 7eqtypi 78 . . 3
96, 8wc 50 . 2
10 weq 41 . . . 4
1110, 2, 6, 5dfov1 74 . . 3
12 weq 41 . . . 4
1312, 3, 8, 7dfov1 74 . . 3
142, 6, 3, 8ax-ceq 51 . . 3
1511, 13, 14syl2anc 19 . 2
161, 4, 9, 15dfov2 75 1
 Colors of variables: type var term Syntax hints:   ht 2  kc 5   ke 7  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-wov 71  ax-eqtypi 77 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  ceq1  89  ceq2  90  oveq123  98  hbc  110  ac  197
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