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Mirrors > Home > ILE Home > Th. List > fneq1 | Unicode version |
Description: Equality theorem for function predicate with domain. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
fneq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funeq 5236 |
. . 3
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2 | dmeq 4827 |
. . . 4
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3 | 2 | eqeq1d 2186 |
. . 3
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4 | 1, 3 | anbi12d 473 |
. 2
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5 | df-fn 5219 |
. 2
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6 | df-fn 5219 |
. 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-fun 5218 df-fn 5219 |
This theorem is referenced by: fneq1d 5306 fneq1i 5310 fn0 5335 feq1 5348 foeq1 5434 f1ocnv 5474 mpteqb 5606 eufnfv 5747 tfr0dm 6322 tfrlemiex 6331 tfr1onlemsucfn 6340 tfr1onlemsucaccv 6341 tfr1onlembxssdm 6343 tfr1onlembfn 6344 tfr1onlemex 6347 tfr1onlemaccex 6348 tfr1onlemres 6349 mapval2 6677 elixp2 6701 ixpfn 6703 elixpsn 6734 cc2lem 7264 cc3 7266 |
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