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Theorem resmpt3 5330
 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 5292 . 2
2 ssid 3528 . . . 4
3 resmpt 5329 . . . 4
42, 3ax-mp 5 . . 3
54reseq1i 5275 . 2
6 inss1 3723 . . 3
7 resmpt 5329 . . 3
86, 7ax-mp 5 . 2
91, 5, 83eqtr3i 2504 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1379   cin 3480   wss 3481   cmpt 4511   cres 5007 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-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  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-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-opab 4512  df-mpt 4513  df-xp 5011  df-rel 5012  df-res 5017 This theorem is referenced by:  offres  6790  lo1resb  13366  o1resb  13368  measinb2  28026  eulerpartgbij  28143
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