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Mirrors > Home > MPE Home > Th. List > strfvn | Structured version Visualization version GIF version |
Description: Value of a structure
component extractor πΈ. Normally, πΈ is a
defined constant symbol such as Base (df-base 17092) and π is the
index of the component. π is a structure, i.e. a specific
member of
a class of structures such as Poset (df-poset 18210) where
π
β Poset.
Hint: Do not substitute π by a specific (positive) integer to be independent of a hard-coded index value. Often, (πΈβndx) can be used instead of π. Alternatively, use strfv 17084 instead of strfvn 17066. (Contributed by NM, 9-Sep-2011.) (Revised by Mario Carneiro, 6-Oct-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
strfvn.f | β’ π β V |
strfvn.c | β’ πΈ = Slot π |
Ref | Expression |
---|---|
strfvn | β’ (πΈβπ) = (πβπ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strfvn.c | . . 3 β’ πΈ = Slot π | |
2 | strfvn.f | . . . 4 β’ π β V | |
3 | 2 | a1i 11 | . . 3 β’ (β€ β π β V) |
4 | 1, 3 | strfvnd 17065 | . 2 β’ (β€ β (πΈβπ) = (πβπ)) |
5 | 4 | mptru 1549 | 1 β’ (πΈβπ) = (πβπ) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 β€wtru 1543 β wcel 2107 Vcvv 3447 βcfv 6500 Slot cslot 17061 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5260 ax-nul 5267 ax-pr 5388 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-opab 5172 df-mpt 5193 df-id 5535 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-iota 6452 df-fun 6502 df-fv 6508 df-slot 17062 |
This theorem is referenced by: str0 17069 ndxarg 17076 setsnid 17089 setsnidOLD 17090 baseval 17093 ressbasOLD 17127 resvsca 32175 |
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