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Theorem ibd 167
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 111 . 2 ((ψχ) → (ψχ))
31, 2syli 33 1 (φ → (ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.21ndd  620  oibabs  799  sssnm  3516
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