Metamath Proof Explorer


Definition df-vhc2

Description: Definition of a 2-element virtual hypotheses collection. (Contributed by Alan Sare, 23-Apr-2015) (New usage is discouraged.)

Ref Expression
Assertion df-vhc2 ( (    𝜑    ,    𝜓    ) ↔ ( 𝜑 ∧ 𝜓 ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 wph ⊢ 𝜑
1 wps ⊢ 𝜓
2 0 1 wvhc2 ⊢ (    𝜑    ,    𝜓    )
3 0 1 wa ⊢ ( 𝜑 ∧ 𝜓 )
4 2 3 wb ⊢ ( (    𝜑    ,    𝜓    ) ↔ ( 𝜑 ∧ 𝜓 ) )