strnfvn - Intuitionistic Logic Explorer

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Theorem strnfvn 11823

Description: Value of a structure component extractor

. Normally,

is a defined constant symbol such as

(df-base 11808) 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 11846. (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 11822	. 2
7	6	mptru 1323	1

Colors of variables: wff set class

Syntax hints:

wceq 1314

wtru 1315

wcel 1463

cvv 2657

cfv 5081

cn 8630 Slot cslot 11801

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-13 1474 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 ax-un 4315

This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-v 2659 df-sbc 2879 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-br 3896 df-opab 3950 df-mpt 3951 df-id 4175 df-xp 4505 df-rel 4506 df-cnv 4507 df-co 4508 df-dm 4509 df-rn 4510 df-iota 5046 df-fun 5083 df-fv 5089 df-slot 11806

This theorem is referenced by: ndxarg 11825 strsl0 11850 baseval 11854

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