Theorem ee101

Description: e101 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee101.1	⊢ ( 𝜑 → 𝜓 )
	ee101.2	⊢ 𝜒
	ee101.3	⊢ ( 𝜑 → 𝜃 )
	ee101.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	ee101	⊢ ( 𝜑 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ee101.1	⊢ ( 𝜑 → 𝜓 )
2		ee101.2	⊢ 𝜒
3		ee101.3	⊢ ( 𝜑 → 𝜃 )
4		ee101.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	2	a1i	⊢ ( 𝜑 → 𝜒 )
6	1 5 3 4	syl3c	⊢ ( 𝜑 → 𝜏 )