Theorem un01

Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	un01.1	⊢ (    (    ⊤    ,    𝜑    )    ▶    𝜓    )
Assertion	un01	⊢ (    𝜑    ▶    𝜓    )

Proof

Step	Hyp	Ref	Expression
1		un01.1	⊢ (    (    ⊤    ,    𝜑    )    ▶    𝜓    )
2		tru	⊢ ⊤
3	2	jctl	⊢ ( 𝜑 → ( ⊤ ∧ 𝜑 ) )
4	1	dfvd2ani	⊢ ( ( ⊤ ∧ 𝜑 ) → 𝜓 )
5	3 4	syl	⊢ ( 𝜑 → 𝜓 )
6	5	dfvd1ir	⊢ (    𝜑    ▶    𝜓    )