Theorem syl6mpi 58

Description: e20 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof shortened by Wolf Lammen, 13-Sep-2012.)

Hypotheses

Ref	Expression
syl6mpi.1	⊢ (φ → (ψ → χ))
syl6mpi.2	⊢ θ
syl6mpi.3	⊢ (χ → (θ → τ))

Assertion

Ref	Expression
syl6mpi	⊢ (φ → (ψ → τ))

Proof of Theorem syl6mpi

Step	Hyp	Ref	Expression
1		syl6mpi.1	. 2 ⊢ (φ → (ψ → χ))
2		syl6mpi.2	. . 3 ⊢ θ
3		syl6mpi.3	. . 3 ⊢ (χ → (θ → τ))
4	2, 3	mpi 16	. 2 ⊢ (χ → τ)
5	1, 4	syl6 29	1 ⊢ (φ → (ψ → τ))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by: (None)