Theorem eel021old 42320

Description: el021old 42321 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eel021.1	⊢ 𝜑
eel021.2	⊢ ((𝜓 ∧ 𝜒) → 𝜃)
eel021.3	⊢ ((𝜑 ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
eel021old	⊢ ((𝜓 ∧ 𝜒) → 𝜏)

Proof of Theorem eel021old

Step	Hyp	Ref	Expression
1		eel021.1	. 2 ⊢ 𝜑
2		eel021.2	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃)
3		eel021.3	. 2 ⊢ ((𝜑 ∧ 𝜃) → 𝜏)
4	1, 2, 3	sylancr 587	1 ⊢ ((𝜓 ∧ 𝜒) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by:  sspwimpcf  42540  suctrALTcf  42542