Theorem ee03 44766

Description: e03 44765 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee03.1	⊢ 𝜑
ee03.2	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
ee03.3	⊢ (𝜑 → (𝜏 → 𝜂))

Assertion

Ref	Expression
ee03	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜂)))

Proof of Theorem ee03

Step	Hyp	Ref	Expression
1		ee03.1	. . . . 5 ⊢ 𝜑
2	1	a1i 11	. . . 4 ⊢ (𝜓 → 𝜑)
3	2	a1d 25	. . 3 ⊢ (𝜓 → (𝜒 → 𝜑))
4	3	a1dd 50	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜑)))
5		ee03.2	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
6		ee03.3	. 2 ⊢ (𝜑 → (𝜏 → 𝜂))
7	4, 5, 6	ee33 44546	1 ⊢ (𝜓 → (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:  ee03an  44768  suctrALT2  44862