Theorem ee323 45490

Description: e323 45747 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee323.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee323.2	⊢ (𝜑 → (𝜓 → 𝜏))
ee323.3	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))
ee323.4	⊢ (𝜃 → (𝜏 → (𝜂 → 𝜁)))

Assertion

Ref	Expression
ee323	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜁)))

Proof of Theorem ee323

Step	Hyp	Ref	Expression
1		ee323.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee323.2	. . 3 ⊢ (𝜑 → (𝜓 → 𝜏))
3	2	a1dd 51	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
4		ee323.3	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))
5		ee323.4	. 2 ⊢ (𝜃 → (𝜏 → (𝜂 → 𝜁)))
6	1, 3, 4, 5	ee333 45489	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜁)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  e323  45747  trintALT  45862