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Theorem dfmpt3 5708
 Description: Alternate definition for the "maps to" notation df-mpt 4512. (Contributed by Mario Carneiro, 30-Dec-2016.)
Assertion
Ref Expression
dfmpt3

Proof of Theorem dfmpt3
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-mpt 4512 . 2
2 elsn 4043 . . . . . . 7
32anbi2i 694 . . . . . 6
43anbi2i 694 . . . . 5
542exbii 1668 . . . 4
6 eliunxp 5145 . . . 4
7 elopab 4760 . . . 4
85, 6, 73bitr4i 277 . . 3
98eqriv 2453 . 2
101, 9eqtr4i 2489 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  {csn 4029  <.cop 4035  U_ciun 4330  {copab 4509  e.cmpt 4510  X.cxp 5002 This theorem is referenced by:  dfmpt  6076  taylpfval  22760  indval2  28028 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-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-sbc 3328  df-csb 3435  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-iun 4332  df-opab 4511  df-mpt 4512  df-xp 5010  df-rel 5011
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