Theorem ee30 42227

Description: e30 42226 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee30.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee30.2	⊢ 𝜏
ee30.3	⊢ (𝜃 → (𝜏 → 𝜂))

Assertion

Ref	Expression
ee30	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

Proof of Theorem ee30

Step	Hyp	Ref	Expression
1		ee30.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee30.2	. . . . 5 ⊢ 𝜏
3	2	a1i 11	. . . 4 ⊢ (𝜒 → 𝜏)
4	3	a1i 11	. . 3 ⊢ (𝜓 → (𝜒 → 𝜏))
5	4	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
6		ee30.3	. 2 ⊢ (𝜃 → (𝜏 → 𝜂))
7	1, 5, 6	ee33 42003	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:  ee30an  42229