Theorem ee201

Description: e201 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee201.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee201.2	⊢ 𝜃
	ee201.3	⊢ ( 𝜑 → 𝜏 )
	ee201.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee201	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee201.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee201.2	⊢ 𝜃
3		ee201.3	⊢ ( 𝜑 → 𝜏 )
4		ee201.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	a1i	⊢ ( 𝜓 → 𝜃 )
6	5	a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
7	3	a1d	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
8	1 6 7 4	ee222	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )