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Mirrors > Home > ILE Home > Th. List > resdifcom | Unicode version |
Description: Commutative law for restriction and difference. (Contributed by AV, 7-Jun-2021.) |
Ref | Expression |
---|---|
resdifcom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indif1 3372 | . 2 | |
2 | df-res 4621 | . 2 | |
3 | df-res 4621 | . . 3 | |
4 | 3 | difeq1i 3241 | . 2 |
5 | 1, 2, 4 | 3eqtr4ri 2202 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 cvv 2730 cdif 3118 cin 3120 cxp 4607 cres 4611 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rab 2457 df-v 2732 df-dif 3123 df-in 3127 df-res 4621 |
This theorem is referenced by: setsfun0 12439 |
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