Theorem ee210

Description: e210 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee210.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee210.2	⊢ ( 𝜑 → 𝜃 )
	ee210.3	⊢ 𝜏
	ee210.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee210	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee210.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee210.2	⊢ ( 𝜑 → 𝜃 )
3		ee210.3	⊢ 𝜏
4		ee210.4	⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	2	a1d	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
6	3	a1i	⊢ ( 𝜓 → 𝜏 )
7	6	a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )
8	1 5 7 4	ee222	⊢ ( 𝜑 → ( 𝜓 → 𝜂 ) )