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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq1 5304 |
. . 3
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2 | rneq 4854 |
. . . 4
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3 | 2 | sseq1d 3184 |
. . 3
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4 | 1, 3 | anbi12d 473 |
. 2
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5 | df-f 5220 |
. 2
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6 | df-f 5220 |
. 2
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7 | 4, 5, 6 | 3bitr4g 223 |
1
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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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-br 4004 df-opab 4065 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-fun 5218 df-fn 5219 df-f 5220 |
This theorem is referenced by: feq1d 5352 feq1i 5358 f00 5407 f0bi 5408 f0dom0 5409 fconstg 5412 f1eq1 5416 fconst2g 5731 tfrcllemsucfn 6353 tfrcllemsucaccv 6354 tfrcllembxssdm 6356 tfrcllembfn 6357 tfrcllemex 6360 tfrcllemaccex 6361 tfrcllemres 6362 tfrcl 6364 elmapg 6660 ac6sfi 6897 updjud 7080 finomni 7137 exmidomni 7139 mkvprop 7155 1fv 10138 isgrpinv 12925 upxp 13708 txcn 13711 dceqnconst 14743 dcapnconst 14744 |
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