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Theorem syl6mpi 58
Description: syl6 29 combined with mpi 15. (Contributed by Alan Sare, 8-Jul-2011.) (Proof shortened by Wolf Lammen, 13-Sep-2012.)
Hypotheses
Ref Expression
syl6mpi.1 (φ → (ψχ))
syl6mpi.2 θ
syl6mpi.3 (χ → (θτ))
Assertion
Ref Expression
syl6mpi (φ → (ψτ))

Proof of Theorem syl6mpi
StepHypRef Expression
1 syl6mpi.1 . 2 (φ → (ψχ))
2 syl6mpi.2 . . 3 θ
3 syl6mpi.3 . . 3 (χ → (θτ))
42, 3mpi 15 . 2 (χτ)
51, 4syl6 29 1 (φ → (ψτ))
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: (None)
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