Theorem ee022

Description: e022 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee022.1	⊢ 𝜑
	ee022.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
	ee022.3	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )
	ee022.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee022	⊢ ( 𝜓 → ( 𝜒 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee022.1	⊢ 𝜑
2		ee022.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
3		ee022.3	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )
4		ee022.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	a1i	⊢ ( 𝜒 → 𝜑 )
6	5	a1i	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
7	6 2 3 4	ee222	⊢ ( 𝜓 → ( 𝜒 → 𝜂 ) )