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Mirrors > Home > MPE Home > Th. List > isf34lem3 | Structured version Visualization version Unicode version |
Description: Lemma for isfin3-4 9204. (Contributed by Stefan O'Rear, 7-Nov-2014.) (Revised by Mario Carneiro, 17-May-2015.) |
Ref | Expression |
---|---|
compss.a |
Ref | Expression |
---|---|
isf34lem3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | compss.a | . . . 4 | |
2 | 1 | compsscnv 9193 | . . 3 |
3 | 2 | imaeq1i 5463 | . 2 |
4 | 1 | compssiso 9196 | . . . 4 [] [] |
5 | isof1o 6573 | . . . 4 [] [] | |
6 | f1of1 6136 | . . . 4 | |
7 | 4, 5, 6 | 3syl 18 | . . 3 |
8 | f1imacnv 6153 | . . 3 | |
9 | 7, 8 | sylan 488 | . 2 |
10 | 3, 9 | syl5eqr 2670 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cdif 3571 wss 3574 cpw 4158 cmpt 4729 ccnv 5113 cima 5117 wf1 5885 wf1o 5887 wiso 5889 [] crpss 6936 |
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-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 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-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-isom 5897 df-rpss 6937 |
This theorem is referenced by: isf34lem5 9200 isf34lem7 9201 isf34lem6 9202 |
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