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Theorem dfov1 74
 Description: Forward direction of df-ov 73. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
dfov1.1 F:(α → (β → ∗))
dfov1.2 A:α
dfov1.3 B:β
dfov1.4 R⊧[AFB]
Assertion
Ref Expression
dfov1 R⊧((FA)B)

Proof of Theorem dfov1
StepHypRef Expression
1 dfov1.4 . 2 R⊧[AFB]
21ax-cb1 29 . . 3 R:∗
3 dfov1.1 . . . 4 F:(α → (β → ∗))
4 dfov1.2 . . . 4 A:α
5 dfov1.3 . . . 4 B:β
63, 4, 5df-ov 73 . . 3 ⊤⊧(( = [AFB])((FA)B))
72, 6a1i 28 . 2 R⊧(( = [AFB])((FA)B))
81, 7ax-eqmp 45 1 R⊧((FA)B)
 Colors of variables: type var term Syntax hints:   → ht 2  ∗hb 3  kc 5   = ke 7  [kbr 9  ⊧wffMMJ2 11  wffMMJ2t 12 This theorem was proved from axioms:  ax-syl 15  ax-trud 26  ax-cb1 29  ax-eqmp 45 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  eqcomi  79  mpbi  82  ceq12  88  leq  91  eqtri  95
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