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 ( ∀ 𝑥 ( 𝑥 = 𝑦𝑦 = 𝑥 ) → [ 𝑦 / 𝑥 ] 𝑦 = 𝑥 )
2 equcomi ( 𝑥 = 𝑦𝑦 = 𝑥 )
3 1 2 mpg [ 𝑦 / 𝑥 ] 𝑦 = 𝑥