Metamath Proof Explorer


Theorem bnj312

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj312 φ ψ χ θ ψ φ χ θ

Proof

Step Hyp Ref Expression
1 3ancoma φ ψ χ ψ φ χ
2 1 anbi1i φ ψ χ θ ψ φ χ θ
3 df-bnj17 φ ψ χ θ φ ψ χ θ
4 df-bnj17 ψ φ χ θ ψ φ χ θ
5 2 3 4 3bitr4i φ ψ χ θ ψ φ χ θ