Theorem ee021

Description: e021 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee021.1	⊢ 𝜑
	ee021.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
	ee021.3	⊢ ( 𝜓 → 𝜏 )
	ee021.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee021	⊢ ( 𝜓 → ( 𝜒 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee021.1	⊢ 𝜑
2		ee021.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
3		ee021.3	⊢ ( 𝜓 → 𝜏 )
4		ee021.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	a1i	⊢ ( 𝜒 → 𝜑 )
6	5	a1i	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
7	3	a1d	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )
8	6 2 7 4	ee222	⊢ ( 𝜓 → ( 𝜒 → 𝜂 ) )