Theorem ee020

Description: e020 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee020.1	⊢ 𝜑
	ee020.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
	ee020.3	⊢ 𝜏
	ee020.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee020	⊢ ( 𝜓 → ( 𝜒 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee020.1	⊢ 𝜑
2		ee020.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
3		ee020.3	⊢ 𝜏
4		ee020.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	a1i	⊢ ( 𝜒 → 𝜑 )
6	5	a1i	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
7	3	a1i	⊢ ( 𝜒 → 𝜏 )
8	7	a1i	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )
9	6 2 8 4	ee222	⊢ ( 𝜓 → ( 𝜒 → 𝜂 ) )