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Theorem eu1 2279
 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 2159 . . 3
21euf 2264 . 2
3 eu1.1 . . 3
43sb8eu 2276 . 2
5 equcom 1688 . . . . . . 7
65imbi2i 304 . . . . . 6
76albii 1572 . . . . 5
83sb6rf 2144 . . . . 5
97, 8anbi12i 679 . . . 4
10 ancom 438 . . . 4
11 albiim 1618 . . . 4
129, 10, 113bitr4i 269 . . 3
1312exbii 1589 . 2
142, 4, 133bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1546  wex 1547  wnf 1550  wsb 1655  weu 2258 This theorem is referenced by:  euex  2281  eu2  2283  kmlem15  8004 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262
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