NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  equsb2 GIF version

Theorem equsb2 2035
Description: Substitution applied to an atomic wff. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equsb2 [y / x]y = x

Proof of Theorem equsb2
StepHypRef Expression
1 sb2 2023 . 2 (x(x = yy = x) → [y / x]y = x)
2 equcomi 1679 . 2 (x = yy = x)
31, 2mpg 1548 1 [y / x]y = x
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  sbco  2083  sbidm  2085
  Copyright terms: Public domain W3C validator