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Theorem brovex 6962
 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:   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)   (,)

Proof of Theorem brovex
StepHypRef Expression
1 df-br 4454 . . 3
2 ne0i 3796 . . . 4
3 brovex.1 . . . . . 6
43mpt2ndm0 6511 . . . . 5
54necon1ai 2698 . . . 4
6 brovex.2 . . . . . . 7
7 brrelex12 5043 . . . . . . 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 1379   wcel 1767   wne 2662  cvv 3118  c0 3790  cop 4039   class class class wbr 4453   wrel 5010  (class class class)co 6295   cmpt2 6297 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-xp 5011  df-rel 5012  df-dm 5015  df-iota 5557  df-fv 5602  df-ov 6298  df-oprab 6299  df-mpt2 6300 This theorem is referenced by:  brovmpt2ex  6963
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