Theorem ee02an

Description: e02an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee02an.1	⊢ 𝜑
	ee02an.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
	ee02an.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
Assertion	ee02an	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		ee02an.1	⊢ 𝜑
2		ee02an.2	⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
3		ee02an.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
5	1 2 4	mpsylsyld	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )