Theorem syl56 30

Description: Combine syl5 28 and syl6 29. (Contributed by NM, 14-Nov-2013.)

Hypotheses

Ref	Expression
syl56.1	⊢ (φ → ψ)
syl56.2	⊢ (χ → (ψ → θ))
syl56.3	⊢ (θ → τ)

Assertion

Ref	Expression
syl56	⊢ (χ → (φ → τ))

Proof of Theorem syl56

Step	Hyp	Ref	Expression
1		syl56.1	. 2 ⊢ (φ → ψ)
2		syl56.2	. . 3 ⊢ (χ → (ψ → θ))
3		syl56.3	. . 3 ⊢ (θ → τ)
4	2, 3	syl6 29	. 2 ⊢ (χ → (ψ → τ))
5	1, 4	syl5 28	1 ⊢ (χ → (φ → 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:  spfw  1691  spw  1694  dvelimhw  1849  dvelimv  1939  ax10  1944  cbv2h  1980  euind  3024  reuind  3040  cores  5085  nchoicelem9  6298  fnfrec  6321