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Theorem bianabs 553
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 289 . 2 (𝜑 → (𝜒 ↔ (𝜑𝜒)))
31, 2bitr4d 184 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  ceqsrexv  2697  opelopab2a  4030  ov  5648  ovg  5667  ltresr  6973
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