This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eel021old

Description: el021old without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eel021.1	⊢ 𝜑
	eel021.2	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
	eel021.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
Assertion	eel021old	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		eel021.1	⊢ 𝜑
2		eel021.2	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
3		eel021.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
4	1 2 3	sylancr	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜏 )