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Theorem mp3and 1246
Description: A deduction based on modus ponens. (Contributed by Mario Carneiro, 24-Dec-2016.)
Hypotheses
Ref Expression
mp3and.1 (𝜑𝜓)
mp3and.2 (𝜑𝜒)
mp3and.3 (𝜑𝜃)
mp3and.4 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
Assertion
Ref Expression
mp3and (𝜑𝜏)

Proof of Theorem mp3and
StepHypRef Expression
1 mp3and.1 . . 3 (𝜑𝜓)
2 mp3and.2 . . 3 (𝜑𝜒)
3 mp3and.3 . . 3 (𝜑𝜃)
41, 2, 33jca 1095 . 2 (𝜑 → (𝜓𝜒𝜃))
5 mp3and.4 . 2 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
64, 5mpd 13 1 (𝜑𝜏)
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:  eqsuptid  6403
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