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Theorem impbid21d 201
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 11 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
3 impbid21d.2 . . 3 (𝜑 → (𝜃𝜒))
43a1d 25 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
52, 4impbidd 200 1 (𝜑 → (𝜓 → (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197
This theorem is referenced by:  impbid  202  pm5.1im  253  rp-fakenanass  37380
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