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Theorem sb8eu 2222
 Description: Variable substitution in uniqueness quantifier. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 7-Oct-2016.)
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 1619 . . . . 5
21sb8 2092 . . . 4
3 sbbi 2071 . . . . . 6
4 sb8eu.1 . . . . . . . 8
54nfsb 2109 . . . . . . 7
6 equsb3 2102 . . . . . . . 8
7 nfv 1619 . . . . . . . 8
86, 7nfxfr 1570 . . . . . . 7
95, 8nfbi 1834 . . . . . 6
103, 9nfxfr 1570 . . . . 5
11 nfv 1619 . . . . 5
12 sbequ 2060 . . . . 5
1310, 11, 12cbval 1984 . . . 4
14 equsb3 2102 . . . . . 6
1514sblbis 2072 . . . . 5
1615albii 1566 . . . 4
172, 13, 163bitri 262 . . 3
1817exbii 1582 . 2
19 df-eu 2208 . 2
20 df-eu 2208 . 2
2118, 19, 203bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540  wex 1541  wnf 1544   wceq 1642  wsb 1648  weu 2204 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  df-eu 2208 This theorem is referenced by:  sb8mo  2223  cbveu  2224  eu1  2225  cbvreu  2833
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