strnfvn - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > strnfvn		Unicode version

Theorem strnfvn 12699

Description: Value of a structure component extractor

. Normally,

is a defined constant symbol such as

(df-base 12684) 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 12723. (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 12698	. 2
7	6	mptru 1373	1

Colors of variables: wff set class

Syntax hints:

wceq 1364

wtru 1365

wcel 2167

cvv 2763

cfv 5258

cn 8990 Slot cslot 12677

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 710 ax-5 1461 ax-7 1462 ax-gen 1463 ax-ie1 1507 ax-ie2 1508 ax-8 1518 ax-10 1519 ax-11 1520 ax-i12 1521 ax-bndl 1523 ax-4 1524 ax-17 1540 ax-i9 1544 ax-ial 1548 ax-i5r 1549 ax-13 2169 ax-14 2170 ax-ext 2178 ax-sep 4151 ax-pow 4207 ax-pr 4242 ax-un 4468

This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1475 df-sb 1777 df-eu 2048 df-mo 2049 df-clab 2183 df-cleq 2189 df-clel 2192 df-nfc 2328 df-ral 2480 df-rex 2481 df-v 2765 df-sbc 2990 df-un 3161 df-in 3163 df-ss 3170 df-pw 3607 df-sn 3628 df-pr 3629 df-op 3631 df-uni 3840 df-br 4034 df-opab 4095 df-mpt 4096 df-id 4328 df-xp 4669 df-rel 4670 df-cnv 4671 df-co 4672 df-dm 4673 df-rn 4674 df-iota 5219 df-fun 5260 df-fv 5266 df-slot 12682

This theorem is referenced by: ndxarg 12701 strsl0 12727 baseval 12731

W3C validator