Theorem ee13an

Description: e13an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee13an.1	⊢ ( 𝜑 → 𝜓 )
	ee13an.2	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
	ee13an.3	⊢ ( ( 𝜓 ∧ 𝜏 ) → 𝜂 )
Assertion	ee13an	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee13an.1	⊢ ( 𝜑 → 𝜓 )
2		ee13an.2	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
3		ee13an.3	⊢ ( ( 𝜓 ∧ 𝜏 ) → 𝜂 )
4	3	ex	⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
5	1 2 4	ee13	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )