![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > setsstrset | Structured version Visualization version GIF version |
Description: Relation between df-sets 17130 and df-strset 36670. 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 36670 | . 2 β’ [π΅ / π΄]structπ = ((π βΎ (V β {(π΄βndx)})) βͺ {β¨(π΄βndx), π΅β©}) | |
2 | setsval 17133 | . 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 2784 | 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 394 = wceq 1533 β wcel 2098 Vcvv 3463 β cdif 3937 βͺ cun 3938 {csn 4624 β¨cop 4630 βΎ cres 5674 βcfv 6542 (class class class)co 7415 sSet csts 17129 ndxcnx 17159 [cstrset 36669 |
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 5294 ax-nul 5301 ax-pr 5423 ax-un 7737 |
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-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3465 df-sbc 3770 df-dif 3943 df-un 3945 df-in 3947 df-ss 3957 df-nul 4319 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-br 5144 df-opab 5206 df-id 5570 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-res 5684 df-iota 6494 df-fun 6544 df-fv 6550 df-ov 7418 df-oprab 7419 df-mpo 7420 df-sets 17130 df-strset 36670 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |