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Theorem resmptf 27320
 Description: Restriction of the mapping operation. (Contributed by Thierry Arnoux, 28-Mar-2017.)
Hypotheses
Ref Expression
resmptf.a
resmptf.b
Assertion
Ref Expression
resmptf

Proof of Theorem resmptf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 resmpt 5329 . 2
2 resmptf.a . . . 4
3 nfcv 2629 . . . 4
4 nfcv 2629 . . . 4
5 nfcsb1v 3456 . . . 4
6 csbeq1a 3449 . . . 4
72, 3, 4, 5, 6cbvmptf 27317 . . 3
87reseq1i 5275 . 2
9 resmptf.b . . 3
10 nfcv 2629 . . 3
119, 10, 4, 5, 6cbvmptf 27317 . 2
121, 8, 113eqtr4g 2533 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379  wnfc 2615  csb 3440   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-sbc 3337  df-csb 3441  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:  esumval  27882  esumel  27883  esumsplit  27888  esumss  27903
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