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Theorem funeu 5617
Description: There is exactly one value of a function. (Contributed by NM, 22-Apr-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
funeu
Distinct variable groups:   ,   ,

Proof of Theorem funeu
StepHypRef Expression
1 funrel 5610 . . . 4
2 releldm 5240 . . . 4
31, 2sylan 471 . . 3
4 eldmg 5203 . . . 4
54ibi 241 . . 3
63, 5syl 16 . 2
7 funmo 5609 . . . 4
87adantr 465 . . 3
9 df-mo 2287 . . 3
108, 9sylib 196 . 2
116, 10mpd 15 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  e.wcel 1818  E!weu 2282  E*wmo 2283   class class class wbr 4452  domcdm 5004  Relwrel 5009  Funwfun 5587
This theorem is referenced by:  funeu2  5618  funbrfv  5911
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-fun 5595
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