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Mirrors > Home > MPE Home > Th. List > s1co | Structured version Visualization version Unicode version |
Description: Mapping of a singleton word. (Contributed by Mario Carneiro, 27-Sep-2015.) (Revised by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
s1co |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | s1val 13378 | . . . . 5 | |
2 | 0cn 10032 | . . . . . 6 | |
3 | xpsng 6406 | . . . . . 6 | |
4 | 2, 3 | mpan 706 | . . . . 5 |
5 | 1, 4 | eqtr4d 2659 | . . . 4 |
6 | 5 | adantr 481 | . . 3 |
7 | 6 | coeq2d 5284 | . 2 |
8 | ffn 6045 | . . . 4 | |
9 | id 22 | . . . 4 | |
10 | fcoconst 6401 | . . . 4 | |
11 | 8, 9, 10 | syl2anr 495 | . . 3 |
12 | fvex 6201 | . . . . 5 | |
13 | s1val 13378 | . . . . 5 | |
14 | 12, 13 | ax-mp 5 | . . . 4 |
15 | c0ex 10034 | . . . . 5 | |
16 | 15, 12 | xpsn 6407 | . . . 4 |
17 | 14, 16 | eqtr4i 2647 | . . 3 |
18 | 11, 17 | syl6reqr 2675 | . 2 |
19 | 7, 18 | eqtr4d 2659 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 csn 4177 cop 4183 cxp 5112 ccom 5118 wfn 5883 wf 5884 cfv 5888 cc 9934 cc0 9936 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-8 1992 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-pow 4843 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-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-s1 13302 |
This theorem is referenced by: cats1co 13601 s2co 13665 frmdgsum 17399 frmdup2 17402 efginvrel2 18140 vrgpinv 18182 frgpup2 18189 mrsubcv 31407 |
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