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Theorem mp3and 1280
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 → ((ψ χ θ) → 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 1132 . 2 (φ → (ψ χ θ))
5 mp3and.4 . 2 (φ → ((ψ χ θ) → τ))
64, 5mpd 14 1 (φτ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by: (None)
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