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Theorem oveq 102
 Description: Equality theorem for binary operation. (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypotheses
Ref Expression
oveq.1 F:(α → (βγ))
oveq.2 A:α
oveq.3 B:β
oveq.4 R⊧[F = S]
Assertion
Ref Expression
oveq R⊧[[AFB] = [ASB]]

Proof of Theorem oveq
StepHypRef Expression
1 oveq.1 . 2 F:(α → (βγ))
2 oveq.2 . 2 A:α
3 oveq.3 . 2 B:β
4 oveq.4 . 2 R⊧[F = S]
54ax-cb1 29 . . 3 R:∗
65, 2eqid 83 . 2 R⊧[A = A]
75, 3eqid 83 . 2 R⊧[B = B]
81, 2, 3, 4, 6, 7oveq123 98 1 R⊧[[AFB] = [ASB]]
 Colors of variables: type var term Syntax hints:   → ht 2   = 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  ax-eqtypri 80 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  imval  146  orval  147  anval  148  dfan2  154
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