Theorem ee001

Description: e001 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee001.1	⊢ 𝜑
	ee001.2	⊢ 𝜓
	ee001.3	⊢ ( 𝜒 → 𝜃 )
	ee001.4	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
Assertion	ee001	⊢ ( 𝜒 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ee001.1	⊢ 𝜑
2		ee001.2	⊢ 𝜓
3		ee001.3	⊢ ( 𝜒 → 𝜃 )
4		ee001.4	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
5	1	a1i	⊢ ( 𝜒 → 𝜑 )
6	2	a1i	⊢ ( 𝜒 → 𝜓 )
7	5 6 3 4	syl3c	⊢ ( 𝜒 → 𝜏 )