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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:(al -> (be -> *))
dfov1.2 |- A:al
dfov1.3 |- B:be
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:(al -> (be -> *))
4 dfov1.2 . . . 4 |- A:al
5 dfov1.3 . . . 4 |- B:be
63, 4, 5df-ov 73 . . 3 |- T. |= (( = [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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