Theorem ee100

Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee100.1	⊢ ( 𝜑 → 𝜓 )
	ee100.2	⊢ 𝜒
	ee100.3	⊢ 𝜃
	ee100.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion	ee100	⊢ ( 𝜑 → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ee100.1	⊢ ( 𝜑 → 𝜓 )
2		ee100.2	⊢ 𝜒
3		ee100.3	⊢ 𝜃
4		ee100.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	2	a1i	⊢ ( 𝜑 → 𝜒 )
6	3	a1i	⊢ ( 𝜑 → 𝜃 )
7	1 5 6 4	syl3c	⊢ ( 𝜑 → 𝜏 )