Theorem ee012

Description: e012 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee012.1	⊢ 𝜑
	ee012.2	⊢ ( 𝜓 → 𝜒 )
	ee012.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
	ee012.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee012	⊢ ( 𝜓 → ( 𝜃 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee012.1	⊢ 𝜑
2		ee012.2	⊢ ( 𝜓 → 𝜒 )
3		ee012.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
4		ee012.4	⊢ ( 𝜑 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5	1	a1i	⊢ ( 𝜃 → 𝜑 )
6	5	a1i	⊢ ( 𝜓 → ( 𝜃 → 𝜑 ) )
7	2	a1d	⊢ ( 𝜓 → ( 𝜃 → 𝜒 ) )
8	6 7 3 4	ee222	⊢ ( 𝜓 → ( 𝜃 → 𝜂 ) )