Metamath Proof Explorer

Theorem spimv

Description: A version of spim with a distinct variable requirement instead of a bound-variable hypothesis. Usage of this theorem is discouraged because it depends on ax-13 . See spimfv and spimvw for versions requiring fewer axioms. (Contributed by NM, 31-Jul-1993) (New usage is discouraged.)

Ref Expression
Hypothesis spimv.1 x = y φ ψ
Assertion spimv x φ ψ


Step Hyp Ref Expression
1 spimv.1 x = y φ ψ
2 nfv x ψ
3 2 1 spim x φ ψ