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Theorem sb8euh 2029
 Description: Variable substitution in unique existential quantifier. (Contributed by NM, 7-Aug-1994.) (Revised by Andrew Salmon, 9-Jul-2011.)
Hypothesis
Ref Expression
sb8euh.1
Assertion
Ref Expression
sb8euh

Proof of Theorem sb8euh
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-17 1506 . . . . 5
21sb8h 1834 . . . 4
3 sbbi 1939 . . . . . 6
4 sb8euh.1 . . . . . . . 8
54hbsb 1929 . . . . . . 7
6 equsb3 1931 . . . . . . . 8
7 ax-17 1506 . . . . . . . 8
86, 7hbxfrbi 1452 . . . . . . 7
95, 8hbbi 1528 . . . . . 6
103, 9hbxfrbi 1452 . . . . 5
11 ax-17 1506 . . . . 5
12 sbequ 1820 . . . . 5
1310, 11, 12cbvalh 1733 . . . 4
14 equsb3 1931 . . . . . 6
1514sblbis 1940 . . . . 5
1615albii 1450 . . . 4
172, 13, 163bitri 205 . . 3
1817exbii 1585 . 2
19 df-eu 2009 . 2
20 df-eu 2009 . 2
2118, 19, 203bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1333  wex 1472  wsb 1742  weu 2006 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009 This theorem is referenced by:  eu1  2031
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