Theorem ee13 42013

Description: e13 42257 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee13.1	⊢ (𝜑 → 𝜓)
ee13.2	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
ee13.3	⊢ (𝜓 → (𝜏 → 𝜂))

Assertion

Ref	Expression
ee13	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜂)))

Proof of Theorem ee13

Step	Hyp	Ref	Expression
1		ee13.2	. 2 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
2		ee13.1	. . 3 ⊢ (𝜑 → 𝜓)
3		ee13.3	. . 3 ⊢ (𝜓 → (𝜏 → 𝜂))
4	2, 3	syl 17	. 2 ⊢ (𝜑 → (𝜏 → 𝜂))
5	1, 4	syl6d 75	1 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜂)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  sbcim2g  42047  ee13an  42259