Theorem ee010

Description: e010 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee010.1	⊢ 𝜑
	ee010.2	⊢ ( 𝜓 → 𝜒 )
	ee010.3	⊢ 𝜃
	ee010.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	ee010	⊢ ( 𝜓 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ee010.1	⊢ 𝜑
2		ee010.2	⊢ ( 𝜓 → 𝜒 )
3		ee010.3	⊢ 𝜃
4		ee010.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	1	a1i	⊢ ( 𝜓 → 𝜑 )
6	3	a1i	⊢ ( 𝜓 → 𝜃 )
7	5 2 6 4	syl3c	⊢ ( 𝜓 → 𝜏 )