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Theorem ibd 176
Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 26-Jun-2004.)
Hypothesis
Ref Expression
ibd.1 (𝜑 → (𝜓 → (𝜓𝜒)))
Assertion
Ref Expression
ibd (𝜑 → (𝜓𝜒))

Proof of Theorem ibd
StepHypRef Expression
1 ibd.1 . 2 (𝜑 → (𝜓 → (𝜓𝜒)))
2 bi1 116 . 2 ((𝜓𝜒) → (𝜓𝜒))
31, 2syli 37 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.21ndd  654  oibabs  834  sssnm  3554
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