Theorem ee03

Description: e03 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee03.1	⊢ 𝜑
	ee03.2	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
	ee03.3	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
Assertion	ee03	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee03.1	⊢ 𝜑
2		ee03.2	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
3		ee03.3	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
4	1	a1i	⊢ ( 𝜓 → 𝜑 )
5	4	a1d	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
6	5	a1dd	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜑 ) ) )
7	6 2 3	ee33	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )