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Theorem eu1 1967
 Description: An alternate way to express uniqueness used by some authors. Exercise 2(b) of [Margaris] p. 110. (Contributed by NM, 20-Aug-1993.)
Hypothesis
Ref Expression
eu1.1
Assertion
Ref Expression
eu1
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem eu1
StepHypRef Expression
1 hbs1 1856 . . 3
21euf 1947 . 2
3 eu1.1 . . 3
43sb8euh 1965 . 2
5 equcom 1634 . . . . . . 7
65imbi2i 224 . . . . . 6
76albii 1400 . . . . 5
83sb6rf 1775 . . . . 5
97, 8anbi12i 448 . . . 4
10 ancom 262 . . . 4
11 albiim 1417 . . . 4
129, 10, 113bitr4i 210 . . 3
1312exbii 1537 . 2
142, 4, 133bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283  wex 1422  wsb 1686  weu 1942 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-eu 1945 This theorem is referenced by:  euex  1972  eu2  1986
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