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Theorem oveq12 100
 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
oveq1.4 R⊧[A = C]
oveq12.5 R⊧[B = T]
Assertion
Ref Expression
oveq12 R⊧[[AFB] = [CFT]]

Proof of Theorem oveq12
StepHypRef Expression
1 oveq.1 . 2 F:(α → (βγ))
2 oveq.2 . 2 A:α
3 oveq.3 . 2 B:β
4 oveq1.4 . . . 4 R⊧[A = C]
54ax-cb1 29 . . 3 R:∗
65, 1eqid 83 . 2 R⊧[F = F]
7 oveq12.5 . 2 R⊧[B = T]
81, 2, 3, 6, 4, 7oveq123 98 1 R⊧[[AFB] = [CFT]]
 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:  oveq2  101  clf  115  imval  146  dfan2  154  ecase  163  exlimdv2  166  eta  178  cbvf  179  leqf  181  exlimd  183  ac  197
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