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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  5416  ovmpt4g  7580  ov3  7596  omeulem2  8620  domtriomlem  10480  nsmallnq  11015  bposlem1  27343  pntrsumbnd  27625  elntg2  29015  mptsnunlem  37321  poimirlem27  37634  refressn  38425  frege92  43945  nzss  44313  modelaxreplem1  44943  setis  48929
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