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Theorem resdifcom 4763
 Description: Commutative law for restriction and difference. (Contributed by AV, 7-Jun-2021.)
Assertion
Ref Expression
resdifcom

Proof of Theorem resdifcom
StepHypRef Expression
1 indif1 3260 . 2
2 df-res 4479 . 2
3 df-res 4479 . . 3
43difeq1i 3129 . 2
51, 2, 43eqtr4ri 2126 1
 Colors of variables: wff set class Syntax hints:   wceq 1296  cvv 2633   cdif 3010   cin 3012   cxp 4465   cres 4469 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-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rab 2379  df-v 2635  df-dif 3015  df-in 3019  df-res 4479 This theorem is referenced by:  setsfun0  11694
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