Theorem ee002

Description: e002 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee002.1	⊢ 𝜑
	ee002.2	⊢ 𝜓
	ee002.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
	ee002.4	⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee002	⊢ ( 𝜒 → ( 𝜃 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee002.1	⊢ 𝜑
2		ee002.2	⊢ 𝜓
3		ee002.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
4		ee002.4	⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
5	1	a1i	⊢ ( 𝜃 → 𝜑 )
6	5	a1i	⊢ ( 𝜒 → ( 𝜃 → 𝜑 ) )
7	2	a1i	⊢ ( 𝜃 → 𝜓 )
8	7	a1i	⊢ ( 𝜒 → ( 𝜃 → 𝜓 ) )
9	6 8 3 4	ee222	⊢ ( 𝜒 → ( 𝜃 → 𝜂 ) )