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Theorem dfmpt3 5569
 Description: Alternate definition for the "maps to" notation df-mpt 4270. (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 4270 . 2
2 elsn 3831 . . . . . . 7
32anbi2i 677 . . . . . 6
43anbi2i 677 . . . . 5
542exbii 1594 . . . 4
6 eliunxp 5014 . . . 4
7 elopab 4464 . . . 4
85, 6, 73bitr4i 270 . . 3
98eqriv 2435 . 2
101, 9eqtr4i 2461 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wceq 1653   wcel 1726  csn 3816  cop 3819  ciun 4095  copab 4267   cmpt 4268   cxp 4878 This theorem is referenced by:  dfmpt  5913  taylpfval  20283  indval2  24414 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-iun 4097  df-opab 4269  df-mpt 4270  df-xp 4886  df-rel 4887
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