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Theorem sb8eu 2301
 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 1630 . . . . 5
21sb8 2170 . . . 4
3 sbbi 2143 . . . . . 6
4 sb8eu.1 . . . . . . . 8
54nfsb 2187 . . . . . . 7
6 equsb3 2180 . . . . . . . 8
7 nfv 1630 . . . . . . . 8
86, 7nfxfr 1580 . . . . . . 7
95, 8nfbi 1857 . . . . . 6
103, 9nfxfr 1580 . . . . 5
11 nfv 1630 . . . . 5
12 sbequ 2113 . . . . 5
1310, 11, 12cbval 1983 . . . 4
14 equsb3 2180 . . . . . 6
1514sblbis 2146 . . . . 5
1615albii 1576 . . . 4
172, 13, 163bitri 264 . . 3
1817exbii 1593 . 2
19 df-eu 2287 . 2
20 df-eu 2287 . 2
2118, 19, 203bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1550  wex 1551  wnf 1554  wsb 1659  weu 2283 This theorem is referenced by:  sb8mo  2302  cbveu  2303  eu1  2304  cbvreu  2932 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287
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