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Theorem mpbidi 244
 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 232 . 2 (𝜑 → (𝜓𝜒))
41, 3sylcom 30 1 (𝜃 → (𝜑𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209 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 210 This theorem is referenced by:  ralxfr2d  5292  ovmpt4g  7279  ov3  7294  omeulem2  8192  domtriomlem  9849  nsmallnq  10384  bposlem1  25857  pntrsumbnd  26139  elntg2  26768  mptsnunlem  34657  poimirlem27  34984  frege92  40489  nzss  40857  setis  45057
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