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Theorem brovex 6969
Description: A binary relation of the value of an operation given by the "maps to" notation. (Contributed by Alexander van der Vekens, 21-Oct-2017.)
Hypotheses
Ref Expression
brovex.1
brovex.2
Assertion
Ref Expression
brovex
Distinct variable group:   ,

Proof of Theorem brovex
StepHypRef Expression
1 df-br 4453 . . 3
2 ne0i 3790 . . . 4
3 brovex.1 . . . . . 6
43mpt2ndm0 6516 . . . . 5
54necon1ai 2688 . . . 4
6 brovex.2 . . . . . . 7
7 brrelex12 5042 . . . . . . 7
86, 7sylan 471 . . . . . 6
9 id 22 . . . . . 6
108, 9syldan 470 . . . . 5
1110ex 434 . . . 4
122, 5, 113syl 20 . . 3
131, 12sylbi 195 . 2
1413pm2.43i 47 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652   cvv 3109   c0 3784  <.cop 4035   class class class wbr 4452  Relwrel 5009  (class class class)co 6296  e.cmpt2 6298
This theorem is referenced by:  brovmpt2ex  6970
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-8 1820  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-pow 4630  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-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-dm 5014  df-iota 5556  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301
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