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Theorem dfov2 67
Description: Reverse direction of df-ov 65.
Hypotheses
Ref Expression
dfov1.1 |- F:(al -> (be -> *))
dfov1.2 |- A:al
dfov1.3 |- B:be
dfov2.4 |- R |= ((FA)B)
Assertion
Ref Expression
dfov2 |- R |= [AFB]
Proof of Theorem dfov2
StepHypRef Expression
1 dfov1.1 . . 3 |- F:(al -> (be -> *))
2 dfov1.2 . . 3 |- A:al
3 dfov1.3 . . 3 |- B:be
41, 2, 3wov 64 . 2 |- [AFB]:*
5 dfov2.4 . 2 |- R |= ((FA)B)
65ax-cb1 29 . . 3 |- R:*
71, 2, 3df-ov 65 . . 3 |- T. |= (( = [AFB])((FA)B))
86, 7a1i 28 . 2 |- R |= (( = [AFB])((FA)B))
94, 5, 8mpbirx 48 1 |- R |= [AFB]
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-jca 17  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-refl 39  ax-eqmp 42  ax-ceq 46
This theorem depends on definitions:  df-ov 65
This theorem is referenced by:  eqcomi  70  eqid  73  ded  74  ceq12  78  leq  81  beta  82  distrc  83  distrl  84  eqtri  85  oveq123  88  hbov  101  ovl  107
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