Theorem ee31 42261

Description: e31 42260 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee31.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee31.2	⊢ (𝜑 → 𝜏)
ee31.3	⊢ (𝜃 → (𝜏 → 𝜂))

Assertion

Ref	Expression
ee31	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

Proof of Theorem ee31

Step	Hyp	Ref	Expression
1		ee31.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee31.2	. . . 4 ⊢ (𝜑 → 𝜏)
3	2	a1d 25	. . 3 ⊢ (𝜑 → (𝜒 → 𝜏))
4	3	a1d 25	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
5		ee31.3	. 2 ⊢ (𝜃 → (𝜏 → 𝜂))
6	1, 4, 5	ee33 42030	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:  trintALT  42390