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Theorem mpsyl 59
Description: Modus ponens combined with a syllogism inference. (Contributed by Alan Sare, 20-Apr-2011.)
Hypotheses
Ref Expression
mpsyl.1 φ
mpsyl.2 (ψχ)
mpsyl.3 (φ → (χθ))
Assertion
Ref Expression
mpsyl (ψθ)

Proof of Theorem mpsyl
StepHypRef Expression
1 mpsyl.1 . . 3 φ
21a1i 9 . 2 (ψφ)
3 mpsyl.2 . 2 (ψχ)
4 mpsyl.3 . 2 (φ → (χθ))
52, 3, 4sylc 56 1 (ψθ)
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:  relcnvtr  4783  relresfld  4790  relcoi1  4792  funco  4883  foimacnv  5087  fvi  5173  isoini2  5401  ovidig  5560  smores2  5850  tfrlem5  5871  cauappcvgprlemm  6616
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