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Theorem impbid21d 126
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 125 1 (𝜑 → (𝜓 → (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  impbid  127  pm5.1im  171
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