strnfvn - Intuitionistic Logic Explorer

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Theorem strnfvn 13373

Description: Value of a structure component extractor

. Normally,

is a defined constant symbol such as

(df-base 13358) 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 13397. (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 13372	. 2
7	6	mptru 1411	1

Colors of variables: wff set class

This proof depends on syntax axioms:

wceq 1402

wtru 1403

wcel 2209

cvv 2821

cfv 5377

cn 9304 Slot cslot 13351

This proof depends on axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 721 ax-5 1500 ax-7 1501 ax-gen 1502 ax-ie1 1546 ax-ie2 1547 ax-8 1557 ax-10 1558 ax-11 1559 ax-i12 1560 ax-bndl 1562 ax-4 1563 ax-17 1579 ax-i9 1583 ax-ial 1587 ax-i5r 1588 ax-14 2212 ax-ext 2220 ax-sep 4249 ax-pow 4311 ax-pr 4346 ax-un 4578

This proof depends on definitions: df-bi 117 df-3an 1011 df-tru 1405 df-nf 1514 df-sb 1816 df-eu 2089 df-mo 2090 df-clab 2225 df-cleq 2231 df-clel 2234 df-nfc 2381 df-ral 2533 df-rex 2534 df-v 2823 df-sbc 3052 df-un 3224 df-in 3226 df-ss 3233 df-pw 3690 df-sn 3715 df-pr 3716 df-op 3718 df-uni 3936 df-br 4131 df-opab 4193 df-mpt 4194 df-id 4438 df-xp 4780 df-rel 4781 df-cnv 4782 df-co 4783 df-dm 4784 df-rn 4785 df-iota 5337 df-fun 5379 df-fv 5385 df-slot 13356

This theorem is used by: ndxarg 13375 strsl0 13401 baseval 13405

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