Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sb7h Structured version   Unicode version

Theorem sb7h 2197
 Description: This version of dfsb7 2198 does not require that and be distinct. This permits it to be used as a definition for substitution in a formalization that omits the logically redundant axiom ax-17 1626 i.e. that doesn't have the concept of a variable not occurring in a wff. (df-sb 1659 is also suitable, but its mixing of free and bound variables is distasteful to some logicians.) (Contributed by NM, 26-Jul-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
sb7h.1
Assertion
Ref Expression
sb7h
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem sb7h
StepHypRef Expression
1 sb7h.1 . . 3
21nfi 1560 . 2
32sb7f 2196 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  wsb 1658 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