Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  equsb3 Structured version   Unicode version

Theorem equsb3 2178
 Description: Substitution applied to an atomic wff. (Contributed by Raph Levien and FL, 4-Dec-2005.)
Assertion
Ref Expression
equsb3
Distinct variable group:   ,

Proof of Theorem equsb3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 equsb3lem 2177 . . 3
21sbbii 1665 . 2
3 nfv 1629 . . 3
43sbco2 2161 . 2
5 equsb3lem 2177 . 2
62, 4, 53bitr3i 267 1
 Colors of variables: wff set class Syntax hints:   wb 177  wsb 1658 This theorem is referenced by:  sb8eu  2299  sb8iota  5418  mo5f  23965  sbeqal1  27566 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
 Copyright terms: Public domain W3C validator