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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 3931 | . . 3 | |
2 | 1 | iotabidv 5109 | . 2 |
3 | df-fv 5131 | . 2 | |
4 | df-fv 5131 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 class class class wbr 3929 cio 5086 cfv 5123 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 |
This theorem is referenced by: fveq1i 5422 fveq1d 5423 fvmptdf 5508 fvmptdv2 5510 isoeq1 5702 oveq 5780 offval 5989 ofrfval 5990 offval3 6032 smoeq 6187 recseq 6203 tfr0dm 6219 tfrlemiex 6228 tfr1onlemex 6244 tfr1onlemaccex 6245 tfrcllemsucaccv 6251 tfrcllembxssdm 6253 tfrcllemex 6257 tfrcllemaccex 6258 tfrcllemres 6259 rdgeq1 6268 rdgivallem 6278 rdgon 6283 rdg0 6284 frec0g 6294 freccllem 6299 frecfcllem 6301 frecsuclem 6303 frecsuc 6304 mapsncnv 6589 elixp2 6596 elixpsn 6629 mapsnen 6705 mapxpen 6742 ac6sfi 6792 updjud 6967 enomnilem 7010 finomni 7012 exmidomni 7014 fodjuomnilemres 7020 infnninf 7022 nnnninf 7023 ismkvnex 7029 mkvprop 7032 fodjumkvlemres 7033 1fv 9916 seqeq3 10223 iseqf1olemjpcl 10268 iseqf1olemqpcl 10269 iseqf1olemfvp 10270 seq3f1olemqsum 10273 seq3f1olemstep 10274 seq3f1olemp 10275 shftvalg 10608 shftval4g 10609 clim 11050 summodc 11152 fsum3 11156 prodmodc 11347 ennnfonelemim 11937 ctinfom 11941 strnfvnd 11979 iscnp 12368 upxp 12441 elcncf 12729 reldvg 12817 subctctexmid 13196 0nninf 13197 nninff 13198 nnsf 13199 peano4nninf 13200 peano3nninf 13201 nninfalllemn 13202 nninfalllem1 13203 nninfself 13209 nninfsellemeq 13210 nninfsellemeqinf 13212 isomninnlem 13225 trilpolemlt1 13234 |
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