Theorem eel0321old 41043

Description: el0321old 41044 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eel0321old.1	⊢ 𝜑
eel0321old.2	⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
eel0321old.3	⊢ ((𝜑 ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
eel0321old	⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜂)

Proof of Theorem eel0321old

Step	Hyp	Ref	Expression
1		eel0321old.1	. 2 ⊢ 𝜑
2		eel0321old.2	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
3		eel0321old.3	. 2 ⊢ ((𝜑 ∧ 𝜏) → 𝜂)
4	1, 2, 3	sylancr 589	1 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜂)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399

This theorem is referenced by:  el0321old  41044  suctrALTcf  41249