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Mirrors > Home > MPE Home > Th. List > tposss | Structured version Visualization version Unicode version |
Description: Subset theorem for transposition. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
tposss | tpos tpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coss1 5277 | . . 3 | |
2 | dmss 5323 | . . . . . 6 | |
3 | cnvss 5294 | . . . . . 6 | |
4 | unss1 3782 | . . . . . 6 | |
5 | resmpt 5449 | . . . . . 6 | |
6 | 2, 3, 4, 5 | 4syl 19 | . . . . 5 |
7 | resss 5422 | . . . . 5 | |
8 | 6, 7 | syl6eqssr 3656 | . . . 4 |
9 | coss2 5278 | . . . 4 | |
10 | 8, 9 | syl 17 | . . 3 |
11 | 1, 10 | sstrd 3613 | . 2 |
12 | df-tpos 7352 | . 2 tpos | |
13 | df-tpos 7352 | . 2 tpos | |
14 | 11, 12, 13 | 3sstr4g 3646 | 1 tpos tpos |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 cun 3572 wss 3574 c0 3915 csn 4177 cuni 4436 cmpt 4729 ccnv 5113 cdm 5114 cres 5116 ccom 5118 tpos ctpos 7351 |
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-br 4654 df-opab 4713 df-mpt 4730 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-tpos 7352 |
This theorem is referenced by: tposeq 7354 |
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