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Theorem rbaibd 544
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 . . 3 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
21biancomd 467 . 2 (𝜑 → (𝜓 ↔ (𝜃𝜒)))
32baibd 543 1 ((𝜑𝜃) → (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:  qsqueeze  12582  o1lo12  14886  incexc2  15184  gexdvds  18700  fsumvma  25795  qusker  30950
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