Theorem un10

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

	Ref	Expression
Hypothesis	un10.1	⊢ (    (    𝜑    ,    ⊤    )    ▶    𝜓    )
Assertion	un10	⊢ (    𝜑    ▶    𝜓    )

Proof

Step	Hyp	Ref	Expression
1		un10.1	⊢ (    (    𝜑    ,    ⊤    )    ▶    𝜓    )
2		tru	⊢ ⊤
3	2	jctr	⊢ ( 𝜑 → ( 𝜑 ∧ ⊤ ) )
4	1	dfvd2ani	⊢ ( ( 𝜑 ∧ ⊤ ) → 𝜓 )
5	3 4	syl	⊢ ( 𝜑 → 𝜓 )
6	5	dfvd1ir	⊢ (    𝜑    ▶    𝜓    )