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Theorem impbid21d 119
Description: Deduce an equivalence from two implications. (Contributed by Wolf Lammen, 12-May-2013.)
Hypotheses
Ref Expression
impbid21d.1 (ψ → (χθ))
impbid21d.2 (φ → (θχ))
Assertion
Ref Expression
impbid21d (φ → (ψ → (χθ)))

Proof of Theorem impbid21d
StepHypRef Expression
1 impbid21d.1 . . 3 (ψ → (χθ))
21a1i 9 . 2 (φ → (ψ → (χθ)))
3 impbid21d.2 . . 3 (φ → (θχ))
43a1d 22 . 2 (φ → (ψ → (θχ)))
52, 4impbidd 118 1 (φ → (ψ → (χθ)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  impbid  120  pm5.1im  162
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