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Theorem eu1 2134
 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.)
Hypothesis
Ref Expression
eu1.1
Assertion
Ref Expression
eu1
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem eu1
StepHypRef Expression
1 nfs1v 2066 . . 3
21euf 2120 . 2
3 eu1.1 . . 3
43sb8eu 2132 . 2
5 equcom 1824 . . . . . . 7
65imbi2i 305 . . . . . 6
76albii 1554 . . . . 5
83sb6rf 1985 . . . . 5
97, 8anbi12i 681 . . . 4
10 ancom 439 . . . 4
11 albiim 1612 . . . 4
129, 10, 113bitr4i 270 . . 3
1312exbii 1580 . 2
142, 4, 133bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537  wnf 1539   wceq 1619  wsb 1882  weu 2114 This theorem is referenced by:  euex  2136  eu2  2138  kmlem15  7674 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118
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