Theorem syl56 34

Description: Combine syl5 32 and syl6 33. (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 33	. 2 ⊢ (𝜒 → (𝜓 → 𝜏))
5	1, 4	syl5 32	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:  cbv2h  1736  cbv2w  1738  euind  2913  reuind  2931  sbcimdv  3016  cores  5107  prnmaxl  7429  prnminu  7430  pc2dvds  12261