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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 5362 |
. . 3
| |
| 2 | rneq 4905 |
. . . 4
| |
| 3 | 2 | sseq1d 3222 |
. . 3
|
| 4 | 1, 3 | anbi12d 473 |
. 2
|
| 5 | df-f 5275 |
. 2
| |
| 6 | df-f 5275 |
. 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 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-ext 2187 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-v 2774 df-un 3170 df-in 3172 df-ss 3179 df-sn 3639 df-pr 3640 df-op 3642 df-br 4045 df-opab 4106 df-rel 4682 df-cnv 4683 df-co 4684 df-dm 4685 df-rn 4686 df-fun 5273 df-fn 5274 df-f 5275 |
| This theorem is referenced by: feq1d 5412 feq1i 5418 f00 5467 f0bi 5468 f0dom0 5469 fconstg 5472 f1eq1 5476 fconst2g 5799 tfrcllemsucfn 6439 tfrcllemsucaccv 6440 tfrcllembxssdm 6442 tfrcllembfn 6443 tfrcllemex 6446 tfrcllemaccex 6447 tfrcllemres 6448 tfrcl 6450 elmapg 6748 ac6sfi 6995 updjud 7184 finomni 7242 exmidomni 7244 mkvprop 7260 1fv 10261 seqf1oglem2 10665 seqf1og 10666 iswrd 10996 isgrpinv 13386 isghm 13579 upxp 14744 txcn 14747 plyf 15209 dceqnconst 15999 dcapnconst 16000 |
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