Metamath Proof Explorer


Theorem equsb1

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker equsb1v if possible. (Contributed by NM, 10-May-1993) (New usage is discouraged.)

Ref Expression
Assertion equsb1
|- [ y / x ] x = y

Proof

Step Hyp Ref Expression
1 sb2
 |-  ( A. x ( x = y -> x = y ) -> [ y / x ] x = y )
2 id
 |-  ( x = y -> x = y )
3 1 2 mpg
 |-  [ y / x ] x = y