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Mirrors > Home > MPE Home > Th. List > f1oeq23 | Structured version Visualization version Unicode version |
Description: Equality theorem for one-to-one onto functions. (Contributed by FL, 14-Jul-2012.) |
Ref | Expression |
---|---|
f1oeq23 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oeq2 6128 | . 2 | |
2 | f1oeq3 6129 | . 2 | |
3 | 1, 2 | sylan9bb 736 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wf1o 5887 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-in 3581 df-ss 3588 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 |
This theorem is referenced by: enfixsn 8069 ackbij2lem2 9062 seqf1o 12842 eulerthlem2 15487 isgim 17704 symgval 17799 islmim 19062 fpwrelmapffs 29509 hgt750lemg 30732 poimirlem3 33412 poimirlem15 33424 eldioph2lem1 37323 |
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