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Mirrors > Home > NFE Home > Th. List > f1funfun | Unicode version |
Description: Two ways to express that a set is one-to-one. Each side is equivalent to Definition 6.4(3) of [TakeutiZaring] p. 24, who use the notation "Un2 (A)" for one-to-one. We do not introduce a separate notation since we rarely use it. (Contributed by set.mm contributors, 13-Aug-2004.) (Revised by Scott Fenton, 18-Apr-2021.) |
Ref | Expression |
---|---|
f1funfun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1 4792 | . 2 | |
2 | ancom 437 | . 2 | |
3 | ssv 3291 | . . . . 5 | |
4 | df-f 4791 | . . . . 5 | |
5 | 3, 4 | mpbiran2 885 | . . . 4 |
6 | funfn 5136 | . . . 4 | |
7 | 5, 6 | bitr4i 243 | . . 3 |
8 | 7 | anbi2i 675 | . 2 |
9 | 1, 2, 8 | 3bitri 262 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 cvv 2859 wss 3257 ccnv 4771 cdm 4772 crn 4773 wfun 4775 wfn 4776 wf 4777 wf1 4778 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-fn 4790 df-f 4791 df-f1 4792 |
This theorem is referenced by: (None) |
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