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Theorem eu1 1922
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 1811 . . 3
21euf 1902 . 2
3 eu1.1 . . 3
43sb8euh 1920 . 2
5 equcom 1590 . . . . . . 7
65imbi2i 215 . . . . . 6
76albii 1356 . . . . 5
83sb6rf 1730 . . . . 5
97, 8anbi12i 433 . . . 4
10 ancom 253 . . . 4
11 albiim 1373 . . . 4
129, 10, 113bitr4i 201 . . 3
1312exbii 1493 . 2
142, 4, 133bitr4i 201 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240  wex 1378  wsb 1642  weu 1897
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900
This theorem is referenced by:  euex  1927  eu2  1941
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