Theorem ee102

Description: e102 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee102.1	⊢ ( 𝜑 → 𝜓 )
	ee102.2	⊢ 𝜒
	ee102.3	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
	ee102.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion	ee102	⊢ ( 𝜑 → ( 𝜃 → 𝜂 ) )

Proof

Step	Hyp	Ref	Expression
1		ee102.1	⊢ ( 𝜑 → 𝜓 )
2		ee102.2	⊢ 𝜒
3		ee102.3	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
4		ee102.4	⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5	1	a1d	⊢ ( 𝜑 → ( 𝜃 → 𝜓 ) )
6	2	a1i	⊢ ( 𝜃 → 𝜒 )
7	6	a1i	⊢ ( 𝜑 → ( 𝜃 → 𝜒 ) )
8	5 7 3 4	ee222	⊢ ( 𝜑 → ( 𝜃 → 𝜂 ) )