Theorem ee011

Description: e011 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee011.1	⊢ 𝜑
	ee011.2	⊢ ( 𝜓 → 𝜒 )
	ee011.3	⊢ ( 𝜓 → 𝜃 )
	ee011.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	ee011	⊢ ( 𝜓 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ee011.1	⊢ 𝜑
2		ee011.2	⊢ ( 𝜓 → 𝜒 )
3		ee011.3	⊢ ( 𝜓 → 𝜃 )
4		ee011.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	1	a1i	⊢ ( 𝜓 → 𝜑 )
6	5 2 3 4	syl3c	⊢ ( 𝜓 → 𝜏 )