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Theorem baibd 875
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baibd.1 (φ → (ψ ↔ (χ θ)))
Assertion
Ref Expression
baibd ((φ χ) → (ψθ))

Proof of Theorem baibd
StepHypRef Expression
1 baibd.1 . 2 (φ → (ψ ↔ (χ θ)))
2 ibar 490 . . 3 (χ → (θ ↔ (χ θ)))
32bicomd 192 . 2 (χ → ((χ θ) ↔ θ))
41, 3sylan9bb 680 1 ((φ χ) → (ψθ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by: (None)
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