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Theorem sb8eu 1988
 Description: Variable substitution in unique existential 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 1491 . . . . 5
21sb8 1810 . . . 4
3 sbbi 1908 . . . . . 6
4 sb8eu.1 . . . . . . . 8
54nfsb 1897 . . . . . . 7
6 equsb3 1900 . . . . . . . 8
7 nfv 1491 . . . . . . . 8
86, 7nfxfr 1433 . . . . . . 7
95, 8nfbi 1551 . . . . . 6
103, 9nfxfr 1433 . . . . 5
11 nfv 1491 . . . . 5
12 sbequ 1794 . . . . 5
1310, 11, 12cbval 1710 . . . 4
14 equsb3 1900 . . . . . 6
1514sblbis 1909 . . . . 5
1615albii 1429 . . . 4
172, 13, 163bitri 205 . . 3
1817exbii 1567 . 2
19 df-eu 1978 . 2
20 df-eu 1978 . 2
2118, 19, 203bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wb 104  wal 1312  wnf 1419  wex 1451  wsb 1718  weu 1975 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978 This theorem is referenced by:  sb8mo  1989  nfeud  1991  nfeu  1994  cbveu  1999  cbvreu  2627  acexmid  5739
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