Theorem ee333 42016

Description: e333 42242 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee333.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee333.2	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
ee333.3	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))
ee333.4	⊢ (𝜃 → (𝜏 → (𝜂 → 𝜁)))

Assertion

Ref	Expression
ee333	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜁)))

Proof of Theorem ee333

Step	Hyp	Ref	Expression
1		ee333.1	. . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	3imp 1109	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
3		ee333.2	. . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
4	3	3imp 1109	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
5		ee333.3	. . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))
6	5	3imp 1109	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜂)
7		ee333.4	. . 3 ⊢ (𝜃 → (𝜏 → (𝜂 → 𝜁)))
8	2, 4, 6, 7	syl3c 66	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜁)
9	8	3exp 1117	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜁)))

Syntax hints:   → wi 4   ∧ w3a 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087

This theorem is referenced by:  ee323  42017  ee123  42272