Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > strnfvnd | Unicode version |
Description: Deduction version of strnfvn 11969. (Contributed by Mario Carneiro, 15-Nov-2014.) (Revised by Jim Kingdon, 19-Jan-2023.) |
Ref | Expression |
---|---|
strnfvnd.c | Slot |
strnfvnd.f | |
strnfvnd.n |
Ref | Expression |
---|---|
strnfvnd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strnfvnd.f | . . 3 | |
2 | 1 | elexd 2694 | . 2 |
3 | strnfvnd.n | . . 3 | |
4 | fvexg 5433 | . . 3 | |
5 | 1, 3, 4 | syl2anc 408 | . 2 |
6 | fveq1 5413 | . . 3 | |
7 | strnfvnd.c | . . . 4 Slot | |
8 | df-slot 11952 | . . . 4 Slot | |
9 | 7, 8 | eqtri 2158 | . . 3 |
10 | 6, 9 | fvmptg 5490 | . 2 |
11 | 2, 5, 10 | syl2anc 408 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cvv 2681 cmpt 3984 cfv 5118 cn 8713 Slot cslot 11947 |
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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-iota 5083 df-fun 5120 df-fv 5126 df-slot 11952 |
This theorem is referenced by: strnfvn 11969 strfvssn 11970 strndxid 11976 strsetsid 11981 strslfvd 11989 strslfv2d 11990 setsslid 11998 setsslnid 11999 ressid 12009 |
Copyright terms: Public domain | W3C validator |