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Metamath Proof Explorer

Theorem nabi2i

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

Ref Expression
Hypotheses nabi2i.1 ⊢ φ ↔ ψ
nabi2i.2 ⊢ χ ⊼ ψ
Assertion nabi2i ⊢ χ ⊼ φ

Proof

Step Hyp Ref Expression
1 nabi2i.1 ⊢ φ ↔ ψ
2 nabi2i.2 ⊢ χ ⊼ ψ
3 1 bicomi ⊢ ψ ↔ φ
4 3 nanbi2i ⊢ χ ⊼ ψ ↔ χ ⊼ φ
5 2 4 mpbi ⊢ χ ⊼ φ