MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  equsb2 Structured version   Visualization version   GIF version

Theorem equsb2 2357
Description: Substitution applied to an atomic wff. (Contributed by NM, 10-May-1993.)
Assertion
Ref Expression
equsb2 [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2
StepHypRef Expression
1 sb2 2340 . 2 (∀𝑥(𝑥 = 𝑦𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2 equcomi 1931 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2mpg 1715 1 [𝑦 / 𝑥]𝑦 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 1867
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868
This theorem is referenced by:  bj-sbidmOLD  32021
  Copyright terms: Public domain W3C validator