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Metamath Proof Explorer

Theorem naim12i

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

Ref Expression
Hypotheses naim12i.1 ⊢ φ → ψ
naim12i.2 ⊢ χ → θ
naim12i.3 ⊢ ψ ⊼ θ
Assertion naim12i ⊢ φ ⊼ χ

Proof

Step Hyp Ref Expression
1 naim12i.1 ⊢ φ → ψ
2 naim12i.2 ⊢ χ → θ
3 naim12i.3 ⊢ ψ ⊼ θ
4 1 3 naim1i ⊢ φ ⊼ θ
5 2 4 naim2i ⊢ φ ⊼ χ