Theorem ee123 45744

Description: e123 45743 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee123.1	⊢ (𝜑 → 𝜓)
ee123.2	⊢ (𝜑 → (𝜒 → 𝜃))
ee123.3	⊢ (𝜑 → (𝜒 → (𝜏 → 𝜂)))
ee123.4	⊢ (𝜓 → (𝜃 → (𝜂 → 𝜁)))

Assertion

Ref	Expression
ee123	⊢ (𝜑 → (𝜒 → (𝜏 → 𝜁)))

Proof of Theorem ee123

Step	Hyp	Ref	Expression
1		ee123.1	. . . 4 ⊢ (𝜑 → 𝜓)
2	1	a1d 26	. . 3 ⊢ (𝜑 → (𝜏 → 𝜓))
3	2	a1d 26	. 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜓)))
4		ee123.2	. . 3 ⊢ (𝜑 → (𝜒 → 𝜃))
5	4	a1dd 51	. 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜃)))
6		ee123.3	. 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜂)))
7		ee123.4	. 2 ⊢ (𝜓 → (𝜃 → (𝜂 → 𝜁)))
8	3, 5, 6, 7	ee333 45489	1 ⊢ (𝜑 → (𝜒 → (𝜏 → 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: (None)