Metamath Proof Explorer


Theorem nabi12i

Description: Constructor rule for -/\ . (Contributed by Anthony Hart, 2-Sep-2011)

Ref Expression
Hypotheses nabi12i.1 ⊢ φ ↔ ψ
nabi12i.2 ⊢ χ ↔ θ
nabi12i.3 ⊢ ψ ⊼ θ
Assertion nabi12i ⊢ φ ⊼ χ

Proof

Step Hyp Ref Expression
1 nabi12i.1 ⊢ φ ↔ ψ
2 nabi12i.2 ⊢ χ ↔ θ
3 nabi12i.3 ⊢ ψ ⊼ θ
4 1 3 nabi1i ⊢ φ ⊼ θ
5 2 4 nabi2i ⊢ φ ⊼ χ