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Theorem mpbidi 140
Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994.)
Hypotheses
Ref Expression
mpbidi.min (θ → (φψ))
mpbidi.maj (φ → (ψχ))
Assertion
Ref Expression
mpbidi (θ → (φχ))

Proof of Theorem mpbidi
StepHypRef Expression
1 mpbidi.min . 2 (θ → (φψ))
2 mpbidi.maj . . 3 (φ → (ψχ))
32biimpd 132 . 2 (φ → (ψχ))
41, 3sylcom 25 1 (θ → (φχ))
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:  tpid3g  3474  ralxfr2d  4162  rexxfr2d  4163  ovmpt4g  5565  ovi3  5579  bj-inf2vnlem1  9430
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