Theorem ee22an

Description: e22an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee22an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee22an.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
	ee22an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
Assertion	ee22an	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		ee22an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee22an.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
3		ee22an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
5	1 2 4	syl6c	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )