Theorem iden2

Description: Virtual deduction identity rule. simpr in conjunction form Virtual Deduction notation. (Contributed by Alan Sare, 5-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	iden2	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜓    )

Proof

Step	Hyp	Ref	Expression
1		simpr	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜓 )
2		dfvd2an	⊢ ( (    (    𝜑    ,    𝜓    )    ▶    𝜓    ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜓 ) )
3	1 2	mpbir	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜓    )