Theorem syl6c 60

Description: Inference combining syl6 29 with contraction. (Contributed by Alan Sare, 2-May-2011.)

Hypotheses

Ref	Expression
syl6c.1	⊢ (φ → (ψ → χ))
syl6c.2	⊢ (φ → (ψ → θ))
syl6c.3	⊢ (χ → (θ → τ))

Assertion

Ref	Expression
syl6c	⊢ (φ → (ψ → τ))

Proof of Theorem syl6c

Step	Hyp	Ref	Expression
1		syl6c.2	. 2 ⊢ (φ → (ψ → θ))
2		syl6c.1	. . 3 ⊢ (φ → (ψ → χ))
3		syl6c.3	. . 3 ⊢ (χ → (θ → τ))
4	2, 3	syl6 29	. 2 ⊢ (φ → (ψ → (θ → τ)))
5	1, 4	mpdd 36	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:  syldd  61  impbidd  181  pm5.21ndd  343  jcad  519  ee22  1362