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Theorem dfmpt 5903
 Description: Alternate definition for the "maps to" notation df-mpt 4260 (although it requires that be a set). (Contributed by NM, 24-Aug-2010.) (Revised by Mario Carneiro, 30-Dec-2016.)
Hypothesis
Ref Expression
dfmpt.1
Assertion
Ref Expression
dfmpt

Proof of Theorem dfmpt
StepHypRef Expression
1 dfmpt3 5559 . 2
2 vex 2951 . . . . 5
3 dfmpt.1 . . . . 5
42, 3xpsn 5902 . . . 4
54a1i 11 . . 3
65iuneq2i 4103 . 2
71, 6eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2948  csn 3806  cop 3809  ciun 4085   cmpt 4258   cxp 4868 This theorem is referenced by:  fnasrn  5904  dfmpt2  6429 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453
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