Theorem e1111

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 6-Mar-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1111.1	⊢ (    𝜑    ▶    𝜓    )
	e1111.2	⊢ (    𝜑    ▶    𝜒    )
	e1111.3	⊢ (    𝜑    ▶    𝜃    )
	e1111.4	⊢ (    𝜑    ▶    𝜏    )
	e1111.5	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) )
Assertion	e1111	⊢ (    𝜑    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e1111.1	⊢ (    𝜑    ▶    𝜓    )
2		e1111.2	⊢ (    𝜑    ▶    𝜒    )
3		e1111.3	⊢ (    𝜑    ▶    𝜃    )
4		e1111.4	⊢ (    𝜑    ▶    𝜏    )
5		e1111.5	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) )
6	1	in1	⊢ ( 𝜑 → 𝜓 )
7	2	in1	⊢ ( 𝜑 → 𝜒 )
8	3	in1	⊢ ( 𝜑 → 𝜃 )
9	4	in1	⊢ ( 𝜑 → 𝜏 )
10	6 7 8 9 5	ee1111	⊢ ( 𝜑 → 𝜂 )
11	10	dfvd1ir	⊢ (    𝜑    ▶    𝜂    )