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Theorem resmptf 4775
 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 4773 . 2
2 resmptf.a . . . 4
3 nfcv 2229 . . . 4
4 nfcv 2229 . . . 4
5 nfcsb1v 2964 . . . 4
6 csbeq1a 2942 . . . 4
72, 3, 4, 5, 6cbvmptf 3938 . . 3
87reseq1i 4722 . 2
9 resmptf.b . . 3
10 nfcv 2229 . . 3
119, 10, 4, 5, 6cbvmptf 3938 . 2
121, 8, 113eqtr4g 2146 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1290  wnfc 2216  csb 2934   wss 3000   cmpt 3905   cres 4454 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-14 1451  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3963  ax-pow 4015  ax-pr 4045 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-sbc 2842  df-csb 2935  df-un 3004  df-in 3006  df-ss 3013  df-pw 3435  df-sn 3456  df-pr 3457  df-op 3459  df-opab 3906  df-mpt 3907  df-xp 4458  df-rel 4459  df-res 4464 This theorem is referenced by: (None)
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