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Mirrors > Home > ILE Home > Th. List > fveq1 | Unicode version |
Description: Equality theorem for function value. (Contributed by NM, 29-Dec-1996.) |
Ref | Expression |
---|---|
fveq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 3766 | . . 3 | |
2 | 1 | iotabidv 4888 | . 2 |
3 | df-fv 4910 | . 2 | |
4 | df-fv 4910 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 class class class wbr 3764 cio 4865 cfv 4902 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 |
This theorem is referenced by: fveq1i 5179 fveq1d 5180 fvmptdf 5258 fvmptdv2 5260 isoeq1 5441 oveq 5518 offval 5719 ofrfval 5720 offval3 5761 smoeq 5905 recseq 5921 tfr0 5937 tfrlemiex 5945 rdgeq1 5958 rdgivallem 5968 rdg0 5974 frec0g 5983 frecsuclem3 5990 frecsuc 5991 ac6sfi 6352 1fv 8996 iseqeq3 9216 shftvalg 9437 shftval4g 9438 clim 9802 |
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