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Theorem mp3an1i 1236
Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005.)
Hypotheses
Ref Expression
mp3an1i.1 𝜓
mp3an1i.2 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
Assertion
Ref Expression
mp3an1i (𝜑 → ((𝜒𝜃) → 𝜏))

Proof of Theorem mp3an1i
StepHypRef Expression
1 mp3an1i.1 . . 3 𝜓
2 mp3an1i.2 . . . 4 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
32com12 30 . . 3 ((𝜓𝜒𝜃) → (𝜑𝜏))
41, 3mp3an1 1230 . 2 ((𝜒𝜃) → (𝜑𝜏))
54com12 30 1 (𝜑 → ((𝜒𝜃) → 𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  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: (None)
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