Theorem ee01an 45435

Description: e01an 45434 without virtual deductions. sylancr 599 is also a form of e01an 45434 without virtual deduction, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee01an.1	⊢ 𝜑
ee01an.2	⊢ (𝜓 → 𝜒)
ee01an.3	⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
ee01an	⊢ (𝜓 → 𝜃)

Proof of Theorem ee01an

Step	Hyp	Ref	Expression
1		ee01an.1	. 2 ⊢ 𝜑
2		ee01an.2	. 2 ⊢ (𝜓 → 𝜒)
3		ee01an.3	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)
4	1, 2, 3	sylancr 599	1 ⊢ (𝜓 → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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

This theorem is used by: (None)