strnfvn - Intuitionistic Logic Explorer

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Theorem strnfvn 11983

Description: Value of a structure component extractor

. Normally,

is a defined constant symbol such as

(df-base 11968) 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 12006. (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 11982	. 2
7	6	mptru 1340	1

Colors of variables: wff set class

Syntax hints:

wceq 1331

wtru 1332

wcel 1480

cvv 2686

cfv 5123

cn 8723 Slot cslot 11961

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355

This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fv 5131 df-slot 11966

This theorem is referenced by: ndxarg 11985 strsl0 12010 baseval 12014

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