Metamath Proof Explorer


Theorem equsb2

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 . Check out equsb1v for a version requiring fewer axioms. (Contributed by NM, 10-May-1993) (New usage is discouraged.)

Ref Expression
Assertion equsb2
|- [ y / x ] y = x

Proof

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