Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > resmpt3 | Structured version Visualization version Unicode version |
Description: Unconditional restriction of the mapping operation. (Contributed by Stefan O'Rear, 24-Jan-2015.) (Proof shortened by Mario Carneiro, 22-Mar-2015.) |
Ref | Expression |
---|---|
resmpt3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resres 5409 | . 2 | |
2 | ssid 3624 | . . . 4 | |
3 | resmpt 5449 | . . . 4 | |
4 | 2, 3 | ax-mp 5 | . . 3 |
5 | 4 | reseq1i 5392 | . 2 |
6 | inss1 3833 | . . 3 | |
7 | resmpt 5449 | . . 3 | |
8 | 6, 7 | ax-mp 5 | . 2 |
9 | 1, 5, 8 | 3eqtr3i 2652 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cin 3573 wss 3574 cmpt 4729 cres 5116 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 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-opab 4713 df-mpt 4730 df-xp 5120 df-rel 5121 df-res 5126 |
This theorem is referenced by: offres 7163 lo1resb 14295 o1resb 14297 measinb2 30286 eulerpartgbij 30434 mptima 39437 imassmpt 39481 limsupresicompt 39988 liminfresicompt 40012 |
Copyright terms: Public domain | W3C validator |