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Mirrors > Home > MPE Home > Th. List > s1fv | Structured version Visualization version Unicode version |
Description: Sole symbol of a singleton word. (Contributed by Stefan O'Rear, 15-Aug-2015.) (Revised by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
s1fv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | s1val 13378 | . . 3 | |
2 | 1 | fveq1d 6193 | . 2 |
3 | 0nn0 11307 | . . 3 | |
4 | fvsng 6447 | . . 3 | |
5 | 3, 4 | mpan 706 | . 2 |
6 | 2, 5 | eqtrd 2656 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 csn 4177 cop 4183 cfv 5888 cc0 9936 cn0 11292 cs1 13294 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-mulcl 9998 ax-i2m1 10004 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-n0 11293 df-s1 13302 |
This theorem is referenced by: lsws1 13391 eqs1 13392 wrdl1s1 13394 ccats1val2 13404 ccat2s1p1 13405 ccat2s1p2 13406 cats1un 13475 revs1 13514 cats1fvn 13603 s2fv0 13632 efgsval2 18146 efgs1 18148 efgsp1 18150 efgsfo 18152 pgpfaclem1 18480 0wlkons1 26982 1wlkdlem4 27000 wlk2v2elem2 27016 signstf0 30645 signstfvn 30646 signsvtn0 30647 signstfvneq0 30649 |
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