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Theorem resmpt3 5184
 Description: Unconditional restriction of the mapping operation. (Contributed by Stefan O'Rear, 24-Jan-2015.) (Proof shortened by Mario Carneiro, 22-Mar-2015.)
Assertion
Ref Expression
resmpt3
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem resmpt3
StepHypRef Expression
1 resres 5151 . 2
2 ssid 3359 . . . 4
3 resmpt 5183 . . . 4
42, 3ax-mp 8 . . 3
54reseq1i 5134 . 2
6 inss1 3553 . . 3
7 resmpt 5183 . . 3
86, 7ax-mp 8 . 2
91, 5, 83eqtr3i 2463 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   cin 3311   wss 3312   cmpt 4258   cres 4872 This theorem is referenced by:  offres  6311  lo1resb  12350  o1resb  12352  measinb2  24569 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  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-opab 4259  df-mpt 4260  df-xp 4876  df-rel 4877  df-res 4882
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