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Theorem bianabs 576
Description: Absorb a hypothesis into the second member of a biconditional. (Contributed by FL, 15-Feb-2007.)
Hypothesis
Ref Expression
bianabs.1 (𝜑 → (𝜓 ↔ (𝜑𝜒)))
Assertion
Ref Expression
bianabs (𝜑 → (𝜓𝜒))

Proof of Theorem bianabs
StepHypRef Expression
1 bianabs.1 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜒)))
2 ibar 295 . 2 (𝜑 → (𝜒 ↔ (𝜑𝜒)))
31, 2bitr4d 189 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ceqsrexv  2738  opelopab2a  4068  ov  5723  ovg  5742  ltresr  7323
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