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Theorem rbaibd 948
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 524 . . 3 (𝜃 → (𝜒 ↔ (𝜒𝜃)))
32bicomd 213 . 2 (𝜃 → ((𝜒𝜃) ↔ 𝜒))
41, 3sylan9bb 735 1 ((𝜑𝜃) → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 384
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  df-an 386
This theorem is referenced by:  qsqueeze  12017  o1lo12  14250  incexc2  14551  gexdvds  17980  fsumvma  24919
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