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Theorem equsb3 2281
 Description: Substitution applied to an atomic wff. (Contributed by Raph Levien and FL, 4-Dec-2005.) Remove dependency on ax-11 1937. (Revised by Wolf Lammen, 21-Sep-2018.)
Assertion
Ref Expression
equsb3
Distinct variable group:   ,

Proof of Theorem equsb3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 equsb3lem 2280 . . 3
21sbbii 1812 . 2
3 sbcom3 2260 . . 3
4 nfv 1769 . . . 4
54sbf 2229 . . 3
63, 5bitri 257 . 2
7 equsb3lem 2280 . 2
82, 6, 73bitr3i 283 1
 Colors of variables: wff setvar class Syntax hints:   wb 189  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-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:  sb8eu  2352  mo3  2356  sb8iota  5560  mo5f  28199  mptsnunlem  31810  wl-equsb3  31954  wl-mo3t  31975  wl-sb8eut  31976  frege55lem1b  36562  sbeqal1  36818
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