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Theorem biadani 819
Description: Inference associated with biadan 818. (Contributed by BJ, 4-Mar-2023.)
Hypothesis
Ref Expression
biadani.1 (𝜑𝜓)
Assertion
Ref Expression
biadani ((𝜓 → (𝜑𝜒)) ↔ (𝜑 ↔ (𝜓𝜒)))

Proof of Theorem biadani
StepHypRef Expression
1 biadani.1 . 2 (𝜑𝜓)
2 biadan 818 . 2 ((𝜑𝜓) ↔ ((𝜓 → (𝜑𝜒)) ↔ (𝜑 ↔ (𝜓𝜒))))
31, 2mpbi 233 1 ((𝜓 → (𝜑𝜒)) ↔ (𝜑 ↔ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  biadanii  821  elelb  34298
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