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Theorem mpbidi 242
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 230 . 2 (𝜑 → (𝜓𝜒))
41, 3sylcom 30 1 (𝜃 → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207
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 208
This theorem is referenced by:  ralxfr2d  5301  ovmpt4g  7286  ov3  7300  omeulem2  8198  domtriomlem  9852  nsmallnq  10387  bposlem1  25787  pntrsumbnd  26069  elntg2  26698  mptsnunlem  34501  poimirlem27  34800  frege92  40179  nzss  40526  setis  44728
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