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Metamath Proof Explorer

Theorem nabi1i

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

Ref Expression
Hypotheses nabi1i.1 ⊢ φ ↔ ψ
nabi1i.2 ⊢ ψ ⊼ χ
Assertion nabi1i ⊢ φ ⊼ χ

Proof

Step Hyp Ref Expression
1 nabi1i.1 ⊢ φ ↔ ψ
2 nabi1i.2 ⊢ ψ ⊼ χ
3 1 bicomi ⊢ ψ ↔ φ
4 3 nanbi1i ⊢ ψ ⊼ χ ↔ φ ⊼ χ
5 2 4 mpbi ⊢ φ ⊼ χ