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Mirrors > Home > MPE Home > Th. List > Mathboxes > setsstrset | Structured version Visualization version GIF version |
Description: Relation between df-sets 17096 and df-strset 36011. 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 36011 | . 2 β’ [π΅ / π΄]structπ = ((π βΎ (V β {(π΄βndx)})) βͺ {β¨(π΄βndx), π΅β©}) | |
2 | setsval 17099 | . 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 2791 | 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 396 = wceq 1541 β wcel 2106 Vcvv 3474 β cdif 3945 βͺ cun 3946 {csn 4628 β¨cop 4634 βΎ cres 5678 βcfv 6543 (class class class)co 7408 sSet csts 17095 ndxcnx 17125 [cstrset 36010 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pr 5427 ax-un 7724 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ral 3062 df-rex 3071 df-rab 3433 df-v 3476 df-sbc 3778 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-opab 5211 df-id 5574 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-res 5688 df-iota 6495 df-fun 6545 df-fv 6551 df-ov 7411 df-oprab 7412 df-mpo 7413 df-sets 17096 df-strset 36011 |
This theorem is referenced by: (None) |
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