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Theorem wl-sb8eut 28858
Description: Substitution of variable in universal quantifier. Closed form of sb8eu 2301. (Contributed by Wolf Lammen, 11-Aug-2019.)
Assertion
Ref Expression
wl-sb8eut

Proof of Theorem wl-sb8eut
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfnf1 1838 . . . . . 6
21nfal 1885 . . . . 5
3 equsb3 2146 . . . . . . 7
43sblbis 2106 . . . . . 6
5 nfa1 1836 . . . . . . . 8
6 sp 1799 . . . . . . . 8
75, 6nfsbd 2157 . . . . . . 7
8 nfvd 1675 . . . . . . 7
97, 8nfbid 1871 . . . . . 6
104, 9nfxfrd 1617 . . . . 5
11 sbequ 2077 . . . . . 6
1211a1i 11 . . . . 5
132, 10, 12cbvald 1985 . . . 4
14 nfv 1674 . . . . . 6
1514sb8 2134 . . . . 5
1615bicomi 202 . . . 4
17 equsb3 2146 . . . . . 6
1817sblbis 2106 . . . . 5
1918albii 1611 . . . 4
2013, 16, 193bitr3g 287 . . 3
2120exbidv 1681 . 2
22 df-eu 2266 . 2
23 df-eu 2266 . 2
2421, 22, 233bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1368  E.wex 1587  F/wnf 1590  [wsb 1702  E!weu 2262
This theorem is referenced by:  wl-sb8mot  28859
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266
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