Metamath Proof Explorer


Theorem wl-clabtv

Description: Using class abstraction in a context, requiring x and ph disjoint, but based on fewer axioms than wl-clabt . (Contributed by Wolf Lammen, 29-May-2023)

Ref Expression
Assertion wl-clabtv φ x | ψ = x | φ ψ

Proof

Step Hyp Ref Expression
1 biimt φ ψ φ ψ
2 1 sbbidv φ y x ψ y x φ ψ
3 df-clab y x | ψ y x ψ
4 df-clab y x | φ ψ y x φ ψ
5 2 3 4 3bitr4g φ y x | ψ y x | φ ψ
6 5 eqrdv φ x | ψ = x | φ ψ