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Theorem euf 2210
 Description: A version of the existential uniqueness definition with a hypothesis instead of a distinct variable condition. (Contributed by NM, 12-Aug-1993.)
Hypothesis
Ref Expression
euf.1
Assertion
Ref Expression
euf
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem euf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2208 . 2
2 euf.1 . . . . 5
3 nfv 1619 . . . . 5
42, 3nfbi 1834 . . . 4
54nfal 1842 . . 3
6 nfv 1619 . . . . 5
7 nfv 1619 . . . . 5
86, 7nfbi 1834 . . . 4
98nfal 1842 . . 3
10 equequ2 1686 . . . . 5
1110bibi2d 309 . . . 4
1211albidv 1625 . . 3
135, 9, 12cbvex 1985 . 2
141, 13bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540  wex 1541  wnf 1544   wceq 1642  weu 2204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208 This theorem is referenced by:  eu1  2225  eumo0  2228
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