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Mirrors > Home > NFE Home > Th. List > qdassr | GIF version |
Description: Two ways to write an unordered quadruple. (Contributed by Mario Carneiro, 5-Jan-2016.) |
Ref | Expression |
---|---|
qdassr | ⊢ ({A, B} ∪ {C, D}) = ({A} ∪ {B, C, D}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unass 3420 | . 2 ⊢ (({A} ∪ {B}) ∪ {C, D}) = ({A} ∪ ({B} ∪ {C, D})) | |
2 | df-pr 3742 | . . 3 ⊢ {A, B} = ({A} ∪ {B}) | |
3 | 2 | uneq1i 3414 | . 2 ⊢ ({A, B} ∪ {C, D}) = (({A} ∪ {B}) ∪ {C, D}) |
4 | tpass 3818 | . . 3 ⊢ {B, C, D} = ({B} ∪ {C, D}) | |
5 | 4 | uneq2i 3415 | . 2 ⊢ ({A} ∪ {B, C, D}) = ({A} ∪ ({B} ∪ {C, D})) |
6 | 1, 3, 5 | 3eqtr4i 2383 | 1 ⊢ ({A, B} ∪ {C, D}) = ({A} ∪ {B, C, D}) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ∪ cun 3207 {csn 3737 {cpr 3738 {ctp 3739 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3or 935 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-tp 3743 |
This theorem is referenced by: (None) |
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