MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eu1 Unicode version

Theorem eu1 2327
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.) (Proof shortened by Wolf Lammen, 29-Oct-2018.)
Hypothesis
Ref Expression
eu1.1
Assertion
Ref Expression
eu1
Distinct variable group:   ,

Proof of Theorem eu1
StepHypRef Expression
1 nfs1v 2181 . . 3
21euf 2292 . 2
3 eu1.1 . . 3
43sb8eu 2318 . 2
53sb6rf 2166 . . . . 5
6 equcom 1794 . . . . . . 7
76imbi2i 312 . . . . . 6
87albii 1640 . . . . 5
95, 8anbi12ci 698 . . . 4
10 albiim 1699 . . . 4
119, 10bitr4i 252 . . 3
1211exbii 1667 . 2
132, 4, 123bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  [wsb 1739  E!weu 2282
This theorem is referenced by:  euexALT  2328  kmlem15  8565
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286
  Copyright terms: Public domain W3C validator