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Mirrors > Home > ILE Home > Th. List > leisorel | Unicode version |
Description: Version of isorel 5702 for strictly increasing functions on the reals. (Contributed by Mario Carneiro, 6-Apr-2015.) (Revised by Mario Carneiro, 9-Sep-2015.) |
Ref | Expression |
---|---|
leisorel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 981 | . . 3 | |
2 | simp3r 1010 | . . 3 | |
3 | simp3l 1009 | . . 3 | |
4 | isorel 5702 | . . . 4 | |
5 | 4 | notbid 656 | . . 3 |
6 | 1, 2, 3, 5 | syl12anc 1214 | . 2 |
7 | simp2l 1007 | . . . 4 | |
8 | 7, 3 | sseldd 3093 | . . 3 |
9 | 7, 2 | sseldd 3093 | . . 3 |
10 | xrlenlt 7822 | . . 3 | |
11 | 8, 9, 10 | syl2anc 408 | . 2 |
12 | simp2r 1008 | . . . 4 | |
13 | isof1o 5701 | . . . . . 6 | |
14 | f1of 5360 | . . . . . 6 | |
15 | 1, 13, 14 | 3syl 17 | . . . . 5 |
16 | 15, 3 | ffvelrnd 5549 | . . . 4 |
17 | 12, 16 | sseldd 3093 | . . 3 |
18 | 15, 2 | ffvelrnd 5549 | . . . 4 |
19 | 12, 18 | sseldd 3093 | . . 3 |
20 | xrlenlt 7822 | . . 3 | |
21 | 17, 19, 20 | syl2anc 408 | . 2 |
22 | 6, 11, 21 | 3bitr4d 219 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 w3a 962 wcel 1480 wss 3066 class class class wbr 3924 wf 5114 wf1o 5117 cfv 5118 wiso 5119 cxr 7792 clt 7793 cle 7794 |
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 603 ax-in2 604 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-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 |
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-dif 3068 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-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-fn 5121 df-f 5122 df-f1 5123 df-f1o 5125 df-fv 5126 df-isom 5127 df-le 7799 |
This theorem is referenced by: seq3coll 10578 summodclem2a 11143 |
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