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Theorem rbaibd 833
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baibd.1 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
Assertion
Ref Expression
rbaibd ((𝜑𝜃) → (𝜓𝜒))

Proof of Theorem rbaibd
StepHypRef Expression
1 baibd.1 . 2 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
2 iba 284 . . 3 (𝜃 → (𝜒 ↔ (𝜒𝜃)))
32bicomd 129 . 2 (𝜃 → ((𝜒𝜃) ↔ 𝜒))
41, 3sylan9bb 435 1 ((𝜑𝜃) → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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