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Mirrors > Home > MPE Home > Th. List > sbthlem7 | Structured version Visualization version Unicode version |
Description: Lemma for sbth 8080. (Contributed by NM, 27-Mar-1998.) |
Ref | Expression |
---|---|
sbthlem.1 | |
sbthlem.2 | |
sbthlem.3 |
Ref | Expression |
---|---|
sbthlem7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funres 5929 | . . 3 | |
2 | funres 5929 | . . 3 | |
3 | dmres 5419 | . . . . . . . . 9 | |
4 | inss1 3833 | . . . . . . . . 9 | |
5 | 3, 4 | eqsstri 3635 | . . . . . . . 8 |
6 | ssrin 3838 | . . . . . . . 8 | |
7 | 5, 6 | ax-mp 5 | . . . . . . 7 |
8 | dmres 5419 | . . . . . . . . 9 | |
9 | inss1 3833 | . . . . . . . . 9 | |
10 | 8, 9 | eqsstri 3635 | . . . . . . . 8 |
11 | sslin 3839 | . . . . . . . 8 | |
12 | 10, 11 | ax-mp 5 | . . . . . . 7 |
13 | 7, 12 | sstri 3612 | . . . . . 6 |
14 | disjdif 4040 | . . . . . 6 | |
15 | 13, 14 | sseqtri 3637 | . . . . 5 |
16 | ss0 3974 | . . . . 5 | |
17 | 15, 16 | ax-mp 5 | . . . 4 |
18 | funun 5932 | . . . 4 | |
19 | 17, 18 | mpan2 707 | . . 3 |
20 | 1, 2, 19 | syl2an 494 | . 2 |
21 | sbthlem.3 | . . 3 | |
22 | 21 | funeqi 5909 | . 2 |
23 | 20, 22 | sylibr 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cab 2608 cvv 3200 cdif 3571 cun 3572 cin 3573 wss 3574 c0 3915 cuni 4436 ccnv 5113 cdm 5114 cres 5116 cima 5117 wfun 5882 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 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-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-fun 5890 |
This theorem is referenced by: sbthlem9 8078 |
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