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Theorem resdmdfsn 4788
 Description: Restricting a relation to its domain without a set is the same as restricting the relation to the universe without this set. (Contributed by AV, 2-Dec-2018.)
Assertion
Ref Expression
resdmdfsn

Proof of Theorem resdmdfsn
StepHypRef Expression
1 indif1 3260 . . . 4
2 incom 3207 . . . . . 6
3 inv1 3338 . . . . . 6
42, 3eqtri 2115 . . . . 5
54difeq1i 3129 . . . 4
61, 5eqtri 2115 . . 3
76reseq2i 4742 . 2
8 resindm 4787 . 2
97, 8syl5reqr 2142 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1296  cvv 2633   cdif 3010   cin 3012  csn 3466   cdm 4467   cres 4469   wrel 4472 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-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-14 1457  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978  ax-pow 4030  ax-pr 4060 This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rex 2376  df-rab 2379  df-v 2635  df-dif 3015  df-un 3017  df-in 3019  df-ss 3026  df-pw 3451  df-sn 3472  df-pr 3473  df-op 3475  df-br 3868  df-opab 3922  df-xp 4473  df-rel 4474  df-dm 4477  df-res 4479 This theorem is referenced by:  funresdfunsnss  5539  funresdfunsndc  6305
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