Theorem ee21an

Description: e21an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee21an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee21an.2	⊢ ( 𝜑 → 𝜃 )
	ee21an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
Assertion	ee21an	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		ee21an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee21an.2	⊢ ( 𝜑 → 𝜃 )
3		ee21an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
5	1 2 4	syl6ci	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )