Metamath Proof Explorer

Theorem dvelimv

Description: Similar to dvelim with first hypothesis replaced by a distinct variable condition. Usage of this theorem is discouraged because it depends on ax-13 . Check out dvelimhw for a version requiring fewer axioms. (Contributed by NM, 25-Jul-2015) (Proof shortened by Wolf Lammen, 30-Apr-2018) (New usage is discouraged.)

Ref Expression
Hypothesis dvelimv.1 z = y φ ψ
Assertion dvelimv ¬ x x = y ψ x ψ


Step Hyp Ref Expression
1 dvelimv.1 z = y φ ψ
2 ax-5 φ x φ
3 2 1 dvelim ¬ x x = y ψ x ψ