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Theorem ibd 260
Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. Deduction associated with ibi 258. (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 biimp 206 . 2 ((𝜓𝜒) → (𝜓𝜒))
31, 2syli 39 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 197
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 198
This theorem is referenced by:  sssn  4554  unblem2  8455  atcv0eq  29572  atcv1  29573  atomli  29575  atcvatlem  29578  ibdr  34638
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