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Theorem mp3an13 1234
Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005.)
Hypotheses
Ref Expression
mp3an13.1 𝜑
mp3an13.2 𝜒
mp3an13.3 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
mp3an13 (𝜓𝜃)

Proof of Theorem mp3an13
StepHypRef Expression
1 mp3an13.1 . 2 𝜑
2 mp3an13.2 . . 3 𝜒
3 mp3an13.3 . . 3 ((𝜑𝜓𝜒) → 𝜃)
42, 3mp3an3 1232 . 2 ((𝜑𝜓) → 𝜃)
51, 4mpan 408 1 (𝜓𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  pitonnlem1p1  6979  mulid1  7081  addltmul  8217  eluzaddi  8594  fz01en  9018  fznatpl1  9039  expubnd  9476  bernneq  9536  bernneq2  9537  dvds0  10122  odd2np1  10183  opoe  10206
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