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Theorem mpbidi 241
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 229 . 2 (𝜑 → (𝜓𝜒))
41, 3sylcom 30 1 (𝜃 → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206
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 207
This theorem is referenced by:  ralxfr2d  5410  ovmpt4g  7580  ov3  7596  omeulem2  8621  domtriomlem  10482  nsmallnq  11017  bposlem1  27328  pntrsumbnd  27610  elntg2  29000  mptsnunlem  37339  poimirlem27  37654  refressn  38444  frege92  43968  nzss  44336  modelaxreplem1  44995  ormklocald  46889  setis  49217
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