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Theorem reusv1 4715
 Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 16-Dec-2012.) (Proof shortened by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
reusv1
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem reusv1
StepHypRef Expression
1 nfra1 2748 . . . 4
21nfmo 2297 . . 3
3 rsp 2758 . . . . . . . 8
43imp3a 421 . . . . . . 7
54com12 29 . . . . . 6
65alrimiv 1641 . . . . 5
7 moeq 3102 . . . . 5
8 moim 2326 . . . . 5
96, 7, 8ee10 1385 . . . 4
109ex 424 . . 3
112, 10rexlimi 2815 . 2
12 mormo 2912 . 2
13 reu5 2913 . . 3
1413rbaib 874 . 2
1511, 12, 143syl 19 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725  wmo 2281  wral 2697  wrex 2698  wreu 2699  wrmo 2700 This theorem is referenced by:  reusv5OLD  4725  cdleme25c  31053  cdleme29c  31074  cdlemefrs29cpre1  31096  cdlemk29-3  31609  cdlemkid5  31633  dihlsscpre  31933  mapdh9a  32489  mapdh9aOLDN  32490 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-ral 2702  df-rex 2703  df-reu 2704  df-rmo 2705  df-v 2950
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