Theorem ee110

Description: e110 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee110.1	⊢ ( 𝜑 → 𝜓 )
	ee110.2	⊢ ( 𝜑 → 𝜒 )
	ee110.3	⊢ 𝜃
	ee110.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	ee110	⊢ ( 𝜑 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ee110.1	⊢ ( 𝜑 → 𝜓 )
2		ee110.2	⊢ ( 𝜑 → 𝜒 )
3		ee110.3	⊢ 𝜃
4		ee110.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	3	a1i	⊢ ( 𝜑 → 𝜃 )
6	1 2 5 4	syl3c	⊢ ( 𝜑 → 𝜏 )