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Theorem sb7f 2197
Description: This version of dfsb7 2199 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 1704 i.e. that doesn't have the concept of a variable not occurring in a wff. (df-sb 1740 is also suitable, but its mixing of free and bound variables is distasteful to some logicians.) (Contributed by NM, 26-Jul-2006.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sb7f.1
Assertion
Ref Expression
sb7f
Distinct variable group:   ,

Proof of Theorem sb7f
StepHypRef Expression
1 sb7f.1 . . . 4
21sb5f 2127 . . 3
32sbbii 1746 . 2
41sbco2 2158 . 2
5 sb5 2174 . 2
63, 4, 53bitr3i 275 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sb7h  2198  dfsb7  2199
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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