Theorem el021old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el021old.1	⊢ 𝜑
	el021old.2	⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜃    )
	el021old.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
Assertion	el021old	⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		el021old.1	⊢ 𝜑
2		el021old.2	⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜃    )
3		el021old.3	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
4	2	dfvd2ani	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
5	1 4 3	sylancr	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜏 )
6	5	dfvd2anir	⊢ (    (    𝜓    ,    𝜒    )    ▶    𝜏    )