Theorem ee32 44757

Description: e32 44756 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee32.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee32.2	⊢ (𝜑 → (𝜓 → 𝜏))
ee32.3	⊢ (𝜃 → (𝜏 → 𝜂))

Assertion

Ref	Expression
ee32	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

Proof of Theorem ee32

Step	Hyp	Ref	Expression
1		ee32.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee32.2	. . 3 ⊢ (𝜑 → (𝜓 → 𝜏))
3	2	a1dd 50	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
4		ee32.3	. 2 ⊢ (𝜃 → (𝜏 → 𝜂))
5	1, 3, 4	ee33 44519	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 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: (None)