strnfvn - Intuitionistic Logic Explorer

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Theorem strnfvn 13053

Description: Value of a structure component extractor

. Normally,

is a defined constant symbol such as

(df-base 13038) and

is a fixed integer such as

is a structure, i.e. a specific member of a class of structures.

Note: Normally, this theorem shouldn't be used outside of this section, because it requires hard-coded index values. Instead, use strslfv 13077. (Contributed by NM, 9-Sep-2011.) (Revised by Jim Kingdon, 19-Jan-2023.) (New usage is discouraged.)

**Hypotheses**
Ref	Expression
strnfvn.f
strnfvn.c	Slot
strnfvn.n

**Assertion**
Ref	Expression
strnfvn

**Proof of Theorem strnfvn**
Step	Hyp	Ref	Expression
1		strnfvn.c	. . 3 Slot
2		strnfvn.f	. . . 4
3	2	a1i 9	. . 3
4		strnfvn.n	. . . 4
5	4	a1i 9	. . 3
6	1, 3, 5	strnfvnd 13052	. 2
7	6	mptru 1404	1

Colors of variables: wff set class

Syntax hints:

wceq 1395

wtru 1396

wcel 2200

cvv 2799

cfv 5318

cn 9110 Slot cslot 13031

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 714 ax-5 1493 ax-7 1494 ax-gen 1495 ax-ie1 1539 ax-ie2 1540 ax-8 1550 ax-10 1551 ax-11 1552 ax-i12 1553 ax-bndl 1555 ax-4 1556 ax-17 1572 ax-i9 1576 ax-ial 1580 ax-i5r 1581 ax-13 2202 ax-14 2203 ax-ext 2211 ax-sep 4202 ax-pow 4258 ax-pr 4293 ax-un 4524

This theorem depends on definitions: df-bi 117 df-3an 1004 df-tru 1398 df-nf 1507 df-sb 1809 df-eu 2080 df-mo 2081 df-clab 2216 df-cleq 2222 df-clel 2225 df-nfc 2361 df-ral 2513 df-rex 2514 df-v 2801 df-sbc 3029 df-un 3201 df-in 3203 df-ss 3210 df-pw 3651 df-sn 3672 df-pr 3673 df-op 3675 df-uni 3889 df-br 4084 df-opab 4146 df-mpt 4147 df-id 4384 df-xp 4725 df-rel 4726 df-cnv 4727 df-co 4728 df-dm 4729 df-rn 4730 df-iota 5278 df-fun 5320 df-fv 5326 df-slot 13036

This theorem is referenced by: ndxarg 13055 strsl0 13081 baseval 13085

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