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Theorem eu1 2164
 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 2045 . . 3
21euf 2149 . 2
3 eu1.1 . . 3
43sb8eu 2161 . 2
5 equcom 1647 . . . . . . 7
65imbi2i 303 . . . . . 6
76albii 1553 . . . . 5
83sb6rf 2031 . . . . 5
97, 8anbi12i 678 . . . 4
10 ancom 437 . . . 4
11 albiim 1598 . . . 4
129, 10, 113bitr4i 268 . . 3
1312exbii 1569 . 2
142, 4, 133bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528  wnf 1531   wceq 1623  wsb 1629  weu 2143 This theorem is referenced by:  euex  2166  eu2  2168  kmlem15  7790 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147
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