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Theorem euequ1 2292
Description: Equality has existential uniqueness. Special case of eueq1 3009 proved using only predicate calculus. (Contributed by Stefan Allan, 4-Dec-2008.)
Assertion
Ref Expression
euequ1
Distinct variable group:   ,

Proof of Theorem euequ1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 a9ev 1656 . 2
2 equtr2 1688 . . 3
32gen2 1547 . 2
4 equequ1 1684 . . 3
54eu4 2243 . 2
61, 3, 5mpbir2an 886 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  wal 1540  wex 1541  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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209
This theorem is referenced by:  copsexg  4607  oprabid  5550  scancan  6331
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