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| Mirrors > Home > ILE Home > Th. List > feq1 | Unicode version | ||
| Description: Equality theorem for functions. (Contributed by NM, 1-Aug-1994.) |
| Ref | Expression |
|---|---|
| feq1 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fneq1 5361 |
. . 3
| |
| 2 | rneq 4904 |
. . . 4
| |
| 3 | 2 | sseq1d 3221 |
. . 3
|
| 4 | 1, 3 | anbi12d 473 |
. 2
|
| 5 | df-f 5274 |
. 2
| |
| 6 | df-f 5274 |
. 2
| |
| 7 | 4, 5, 6 | 3bitr4g 223 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-v 2773 df-un 3169 df-in 3171 df-ss 3178 df-sn 3638 df-pr 3639 df-op 3641 df-br 4044 df-opab 4105 df-rel 4681 df-cnv 4682 df-co 4683 df-dm 4684 df-rn 4685 df-fun 5272 df-fn 5273 df-f 5274 |
| This theorem is referenced by: feq1d 5411 feq1i 5417 f00 5466 f0bi 5467 f0dom0 5468 fconstg 5471 f1eq1 5475 fconst2g 5798 tfrcllemsucfn 6438 tfrcllemsucaccv 6439 tfrcllembxssdm 6441 tfrcllembfn 6442 tfrcllemex 6445 tfrcllemaccex 6446 tfrcllemres 6447 tfrcl 6449 elmapg 6747 ac6sfi 6994 updjud 7183 finomni 7241 exmidomni 7243 mkvprop 7259 1fv 10260 seqf1oglem2 10663 seqf1og 10664 iswrd 10994 isgrpinv 13357 isghm 13550 upxp 14715 txcn 14718 plyf 15180 dceqnconst 15961 dcapnconst 15962 |
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