Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fnsnsplitdc | Unicode version |
Description: Split a function into a single point and all the rest. (Contributed by Stefan O'Rear, 27-Feb-2015.) (Revised by Jim Kingdon, 29-Jan-2023.) |
Ref | Expression |
---|---|
fnsnsplitdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnresdm 5281 | . . 3 | |
2 | 1 | 3ad2ant2 1004 | . 2 DECID |
3 | resundi 4881 | . . 3 | |
4 | dcdifsnid 6453 | . . . . 5 DECID | |
5 | 4 | 3adant2 1001 | . . . 4 DECID |
6 | 5 | reseq2d 4868 | . . 3 DECID |
7 | fnressn 5655 | . . . . 5 | |
8 | 7 | uneq2d 3262 | . . . 4 |
9 | 8 | 3adant1 1000 | . . 3 DECID |
10 | 3, 6, 9 | 3eqtr3a 2214 | . 2 DECID |
11 | 2, 10 | eqtr3d 2192 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 DECID wdc 820 w3a 963 wceq 1335 wcel 2128 wral 2435 cdif 3099 cun 3100 csn 3561 cop 3564 cres 4590 wfn 5167 cfv 5172 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-reu 2442 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-f 5176 df-f1 5177 df-fo 5178 df-f1o 5179 df-fv 5180 |
This theorem is referenced by: funresdfunsndc 6455 |
Copyright terms: Public domain | W3C validator |