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Mirrors > Home > MPE Home > Th. List > sbthlem6 | 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 |
---|---|
sbthlem6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 5127 | . . . . 5 | |
2 | sbthlem.1 | . . . . . 6 | |
3 | sbthlem.2 | . . . . . 6 | |
4 | 2, 3 | sbthlem4 8073 | . . . . 5 |
5 | 1, 4 | syl5reqr 2671 | . . . 4 |
6 | 5 | uneq2d 3767 | . . 3 |
7 | rnun 5541 | . . . 4 | |
8 | sbthlem.3 | . . . . 5 | |
9 | 8 | rneqi 5352 | . . . 4 |
10 | df-ima 5127 | . . . . 5 | |
11 | 10 | uneq1i 3763 | . . . 4 |
12 | 7, 9, 11 | 3eqtr4i 2654 | . . 3 |
13 | 6, 12 | syl6reqr 2675 | . 2 |
14 | imassrn 5477 | . . . 4 | |
15 | sstr2 3610 | . . . 4 | |
16 | 14, 15 | ax-mp 5 | . . 3 |
17 | undif 4049 | . . 3 | |
18 | 16, 17 | sylib 208 | . 2 |
19 | 13, 18 | sylan9eqr 2678 | 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 wss 3574 cuni 4436 ccnv 5113 cdm 5114 crn 5115 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-uni 4437 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-rn 5125 df-res 5126 df-ima 5127 df-fun 5890 |
This theorem is referenced by: sbthlem9 8078 |
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