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Mirrors > Home > MPE Home > Th. List > dffo2 | Structured version Visualization version Unicode version |
Description: Alternate definition of an onto function. (Contributed by NM, 22-Mar-2006.) |
Ref | Expression |
---|---|
dffo2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fof 6115 | . . 3 | |
2 | forn 6118 | . . 3 | |
3 | 1, 2 | jca 554 | . 2 |
4 | ffn 6045 | . . 3 | |
5 | df-fo 5894 | . . . 4 | |
6 | 5 | biimpri 218 | . . 3 |
7 | 4, 6 | sylan 488 | . 2 |
8 | 3, 7 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 crn 5115 wfn 5883 wf 5884 wfo 5886 |
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-f 5892 df-fo 5894 |
This theorem is referenced by: foco 6125 foconst 6126 dff1o5 6146 dffo3 6374 dffo4 6375 exfo 6377 fo1stres 7192 fo2ndres 7193 fo2ndf 7284 cantnf 8590 hsmexlem2 9249 setcepi 16738 odf1o1 17987 efgsfo 18152 pjfo 20059 xrhmeo 22745 grpofo 27353 cnpconn 31212 lnmepi 37655 dffo3f 39364 fargshiftfo 41378 |
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