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Theorem sb7f 1967
 Description: This version of dfsb7 1966 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 1506 i.e. that doesn't have the concept of a variable not occurring in a wff. (df-sb 1736 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
sb7f.1
Assertion
Ref Expression
sb7f
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sb7f
StepHypRef Expression
1 sb5 1859 . . 3
21sbbii 1738 . 2
3 sb7f.1 . . 3
43sbco2vh 1918 . 2
5 sb5 1859 . 2
62, 4, 53bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329  wex 1468  wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736 This theorem is referenced by: (None)
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