Metamath Proof Explorer

Theorem nfs1v

Description: The setvar x is not free in [ y / x ] ph when x and y are distinct. (Contributed by Mario Carneiro, 11-Aug-2016) Shorten nfs1v and hbs1 combined. (Revised by Wolf Lammen, 28-Jul-2022)

Ref Expression
Assertion nfs1v x y x φ


Step Hyp Ref Expression
1 sb6 y x φ x x = y φ
2 nfa1 x x x = y φ
3 1 2 nfxfr x y x φ