Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > f1co | Unicode version |
Description: Composition of one-to-one functions. Exercise 30 of [TakeutiZaring] p. 25. (Contributed by NM, 28-May-1998.) |
Ref | Expression |
---|---|
f1co |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1 5123 | . . 3 | |
2 | df-f1 5123 | . . 3 | |
3 | fco 5283 | . . . . 5 | |
4 | funco 5158 | . . . . . . 7 | |
5 | cnvco 4719 | . . . . . . . 8 | |
6 | 5 | funeqi 5139 | . . . . . . 7 |
7 | 4, 6 | sylibr 133 | . . . . . 6 |
8 | 7 | ancoms 266 | . . . . 5 |
9 | 3, 8 | anim12i 336 | . . . 4 |
10 | 9 | an4s 577 | . . 3 |
11 | 1, 2, 10 | syl2anb 289 | . 2 |
12 | df-f1 5123 | . 2 | |
13 | 11, 12 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 ccnv 4533 ccom 4538 wfun 5112 wf 5114 wf1 5115 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 |
This theorem is referenced by: f1oco 5383 tposf12 6159 domtr 6672 djudom 6971 difinfsn 6978 |
Copyright terms: Public domain | W3C validator |