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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > disjALTVidres | Structured version Visualization version GIF version |
Description: The class of identity relations restricted is disjoint. (Contributed by Peter Mazsa, 28-Jun-2020.) (Revised by Peter Mazsa, 27-Sep-2021.) |
Ref | Expression |
---|---|
disjALTVidres | ⊢ Disj ( I ↾ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | disjALTVid 38279 | . 2 ⊢ Disj I | |
2 | disjimres 38274 | . 2 ⊢ ( Disj I → Disj ( I ↾ 𝐴)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Disj ( I ↾ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: I cid 5570 ↾ cres 5675 Disj wdisjALTV 37735 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5295 ax-nul 5302 ax-pr 5424 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3465 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-nul 4320 df-if 4526 df-sn 4626 df-pr 4628 df-op 4632 df-br 5145 df-opab 5207 df-id 5571 df-xp 5679 df-rel 5680 df-cnv 5681 df-co 5682 df-dm 5683 df-rn 5684 df-res 5685 df-coss 37935 df-cnvrefrel 38051 df-funALTV 38206 df-disjALTV 38229 |
This theorem is referenced by: eqvrel1cossidres 38314 detidres 38319 petidres2 38342 |
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