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Theorem sb7f 2120
 Description: This version of dfsb7 2119 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 1616 i.e. that doesn't have the concept of a variable not occurring in a wff. (df-sb 1649 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 groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sb7f
StepHypRef Expression
1 sb5 2100 . . 3
21sbbii 1653 . 2
3 sb7f.1 . . 3
43sbco2 2086 . 2
5 sb5 2100 . 2
62, 4, 53bitr3i 266 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541  wnf 1544  wsb 1648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by:  sb7h  2121
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