Theorem ee30

Description: e30 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee30.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee30.2	⊢ 𝜏
	ee30.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
Assertion	ee30	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee30.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee30.2	⊢ 𝜏
3		ee30.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
4	2	a1i	⊢ ( 𝜒 → 𝜏 )
5	4	a1i	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )
6	5	a1i	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )
7	1 6 3	ee33	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜂 ) ) )