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Mirrors > Home > MPE Home > Th. List > Mathboxes > setsstrset | Structured version Visualization version GIF version |
Description: Relation between df-sets 17106 and df-strset 36523. Temporary theorem kept during the transition from the former to the latter. (Contributed by BJ, 13-Feb-2022.) |
Ref | Expression |
---|---|
setsstrset | β’ ((π β π β§ π΅ β π) β [π΅ / π΄]structπ = (π sSet β¨(π΄βndx), π΅β©)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-strset 36523 | . 2 β’ [π΅ / π΄]structπ = ((π βΎ (V β {(π΄βndx)})) βͺ {β¨(π΄βndx), π΅β©}) | |
2 | setsval 17109 | . 2 β’ ((π β π β§ π΅ β π) β (π sSet β¨(π΄βndx), π΅β©) = ((π βΎ (V β {(π΄βndx)})) βͺ {β¨(π΄βndx), π΅β©})) | |
3 | 1, 2 | eqtr4id 2785 | 1 β’ ((π β π β§ π΅ β π) β [π΅ / π΄]structπ = (π sSet β¨(π΄βndx), π΅β©)) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β§ wa 395 = wceq 1533 β wcel 2098 Vcvv 3468 β cdif 3940 βͺ cun 3941 {csn 4623 β¨cop 4629 βΎ cres 5671 βcfv 6537 (class class class)co 7405 sSet csts 17105 ndxcnx 17135 [cstrset 36522 |
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 2163 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pr 5420 ax-un 7722 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2704 df-cleq 2718 df-clel 2804 df-nfc 2879 df-ral 3056 df-rex 3065 df-rab 3427 df-v 3470 df-sbc 3773 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-if 4524 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-br 5142 df-opab 5204 df-id 5567 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-res 5681 df-iota 6489 df-fun 6539 df-fv 6545 df-ov 7408 df-oprab 7409 df-mpo 7410 df-sets 17106 df-strset 36523 |
This theorem is referenced by: (None) |
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