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Metamath Proof Explorer

Theorem dfvd2an

Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion dfvd2an ⊢ φ ψ → χ ↔ φ ∧ ψ → χ

Proof

Step Hyp Ref Expression
1 df-vd1 ⊢ φ ψ → χ ↔ φ ψ → χ
2 df-vhc2 ⊢ φ ψ ↔ φ ∧ ψ
3 2 imbi1i ⊢ φ ψ → χ ↔ φ ∧ ψ → χ
4 1 3 bitri ⊢ φ ψ → χ ↔ φ ∧ ψ → χ