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Theorem sb8eu 2352
 Description: Variable substitution in uniqueness quantifier. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof shortened by Wolf Lammen, 24-Aug-2019.)
Hypothesis
Ref Expression
sb8eu.1
Assertion
Ref Expression
sb8eu

Proof of Theorem sb8eu
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1769 . . . . 5
21sb8 2273 . . . 4
3 equsb3 2281 . . . . . 6
43sblbis 2253 . . . . 5
54albii 1699 . . . 4
6 sb8eu.1 . . . . . . 7
76nfsb 2289 . . . . . 6
8 nfv 1769 . . . . . 6
97, 8nfbi 2037 . . . . 5
10 nfv 1769 . . . . 5
11 sbequ 2225 . . . . . 6
12 equequ1 1875 . . . . . 6
1311, 12bibi12d 328 . . . . 5
149, 10, 13cbval 2127 . . . 4
152, 5, 143bitri 279 . . 3
1615exbii 1726 . 2
17 df-eu 2323 . 2
18 df-eu 2323 . 2
1916, 17, 183bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wb 189  wal 1450  wex 1671  wnf 1675  wsb 1805  weu 2319 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-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323 This theorem is referenced by:  sb8mo  2353  cbveu  2354  eu1  2359  cbvreu  3003
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