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Theorem mp2d 41
Description: A double modus ponens deduction. (Contributed by NM, 23-May-2013.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)
Hypotheses
Ref Expression
mp2d.1 (φψ)
mp2d.2 (φχ)
mp2d.3 (φ → (ψ → (χθ)))
Assertion
Ref Expression
mp2d (φθ)

Proof of Theorem mp2d
StepHypRef Expression
1 mp2d.1 . 2 (φψ)
2 mp2d.2 . . 3 (φχ)
3 mp2d.3 . . 3 (φ → (ψ → (χθ)))
42, 3mpid 37 . 2 (φ → (ψθ))
51, 4mpd 13 1 (φθ)
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  prloc  6345
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