Theorem el2122old

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

	Ref	Expression
Hypotheses	el2122old.1	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜒    )
	el2122old.2	⊢ (    𝜓    ▶    𝜃    )
	el2122old.3	⊢ (    𝜓    ▶    𝜏    )
	el2122old.4	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜂 )
Assertion	el2122old	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		el2122old.1	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜒    )
2		el2122old.2	⊢ (    𝜓    ▶    𝜃    )
3		el2122old.3	⊢ (    𝜓    ▶    𝜏    )
4		el2122old.4	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜂 )
5	1	dfvd2ani	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
6	2	in1	⊢ ( 𝜓 → 𝜃 )
7	3	in1	⊢ ( 𝜓 → 𝜏 )
8	5 6 7 4	eel2122old	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜂 )
9	8	dfvd2anir	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜂    )