Theorem ee200

Description: e200 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee200.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee200.2	⊢ 𝜃
	ee200.3	⊢ 𝜏
	ee200.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee200	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee200.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee200.2	⊢ 𝜃
3		ee200.3	⊢ 𝜏
4		ee200.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	a1i	⊢ ( 𝜓 → 𝜃 )
6	5	a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
7	3	a1i	⊢ ( 𝜓 → 𝜏 )
8	7	a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
9	1 6 8 4	ee222	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )