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Theorem sb7h 2303
 Description: This version of dfsb7 2304 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-5 1766 i.e. that doesn't have the concept of a variable not occurring in a wff. (df-sb 1806 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 1682 . 2
32sb7f 2302 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450  wex 1671  wsb 1805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806 This theorem is referenced by: (None)
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