Theorem ee20an

Description: e20an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee20an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	ee20an.2	⊢ 𝜃
	ee20an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
Assertion	ee20an	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		ee20an.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ee20an.2	⊢ 𝜃
3		ee20an.3	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
5	1 2 4	syl6mpi	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )