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Theorem resundir 4654
 Description: Distributive law for restriction over union. (Contributed by NM, 23-Sep-2004.)
Assertion
Ref Expression
resundir

Proof of Theorem resundir
StepHypRef Expression
1 indir 3214 . 2
2 df-res 4385 . 2
3 df-res 4385 . . 3
4 df-res 4385 . . 3
53, 4uneq12i 3123 . 2
61, 2, 53eqtr4i 2086 1
 Colors of variables: wff set class Syntax hints:   wceq 1259  cvv 2574   cun 2943   cin 2944   cxp 4371   cres 4375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-res 4385 This theorem is referenced by:  imaundir  4765  fvunsng  5385  fvsnun1  5388  fvsnun2  5389  fsnunfv  5391  fsnunres  5392  fseq1p1m1  9058
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