Theorem ee220

Description: e220 without virtual deductions. (Contributed by Alan Sare, 12-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee220.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee220.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
	ee220.3	⊢ 𝜏
	ee220.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee220	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee220.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee220.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
3		ee220.3	⊢ 𝜏
4		ee220.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	3	2a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
6	1 2 5 4	ee222	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )