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Theorem eu1 2359
 Description: An alternate way to express uniqueness used by some authors. Exercise 2(b) of [Margaris] p. 110. (Contributed by NM, 20-Aug-1993.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof shortened by Wolf Lammen, 29-Oct-2018.)
Hypothesis
Ref Expression
eu1.1
Assertion
Ref Expression
eu1
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem eu1
StepHypRef Expression
1 nfs1v 2286 . . 3
21euf 2327 . 2
3 eu1.1 . . 3
43sb8eu 2352 . 2
53sb6rf 2272 . . . . 5
6 equcom 1870 . . . . . . 7
76imbi2i 319 . . . . . 6
87albii 1699 . . . . 5
95, 8anbi12ci 712 . . . 4
10 albiim 1760 . . . 4
119, 10bitr4i 260 . . 3
1211exbii 1726 . 2
132, 4, 123bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450  wex 1671  wnf 1675  wsb 1805  weu 2319 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323 This theorem is referenced by:  euexALT  2360  kmlem15  8612
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