Metamath Proof Explorer


Theorem bnj982

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypotheses bnj982.1 φ x φ
bnj982.2 ψ x ψ
bnj982.3 χ x χ
bnj982.4 θ x θ
Assertion bnj982 φ ψ χ θ x φ ψ χ θ

Proof

Step Hyp Ref Expression
1 bnj982.1 φ x φ
2 bnj982.2 ψ x ψ
3 bnj982.3 χ x χ
4 bnj982.4 θ x θ
5 df-bnj17 φ ψ χ θ φ ψ χ θ
6 1 2 3 hb3an φ ψ χ x φ ψ χ
7 6 4 hban φ ψ χ θ x φ ψ χ θ
8 5 7 hbxfrbi φ ψ χ θ x φ ψ χ θ