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Theorem mpbidi 144
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 136 . 2 (𝜑 → (𝜓𝜒))
41, 3sylcom 28 1 (𝜃 → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  tpid3g  3511  ralxfr2d  4224  rexxfr2d  4225  ovmpt4g  5651  ovi3  5665  bj-inf2vnlem1  10482
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