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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 3895 |
. . 3
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2 | 1 | iotabidv 5065 |
. 2
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3 | df-fv 5087 |
. 2
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4 | df-fv 5087 |
. 2
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5 | 2, 3, 4 | 3eqtr4g 2170 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-rex 2394 df-uni 3701 df-br 3894 df-iota 5044 df-fv 5087 |
This theorem is referenced by: fveq1i 5374 fveq1d 5375 fvmptdf 5460 fvmptdv2 5462 isoeq1 5654 oveq 5732 offval 5941 ofrfval 5942 offval3 5983 smoeq 6138 recseq 6154 tfr0dm 6170 tfrlemiex 6179 tfr1onlemex 6195 tfr1onlemaccex 6196 tfrcllemsucaccv 6202 tfrcllembxssdm 6204 tfrcllemex 6208 tfrcllemaccex 6209 tfrcllemres 6210 rdgeq1 6219 rdgivallem 6229 rdgon 6234 rdg0 6235 frec0g 6245 freccllem 6250 frecfcllem 6252 frecsuclem 6254 frecsuc 6255 mapsncnv 6540 elixp2 6547 elixpsn 6580 mapsnen 6656 mapxpen 6692 ac6sfi 6742 updjud 6916 enomnilem 6957 finomni 6959 exmidomni 6961 fodjuomnilemres 6967 infnninf 6969 nnnninf 6970 mkvprop 6978 fodjumkvlemres 6979 1fv 9802 seqeq3 10109 iseqf1olemjpcl 10154 iseqf1olemqpcl 10155 iseqf1olemfvp 10156 seq3f1olemqsum 10159 seq3f1olemstep 10160 seq3f1olemp 10161 shftvalg 10494 shftval4g 10495 clim 10935 summodc 11037 fsum3 11041 ennnfonelemim 11775 ctinfom 11779 strnfvnd 11815 iscnp 12203 upxp 12276 elcncf 12539 reldvg 12596 0nninf 12874 nninff 12875 nnsf 12876 peano4nninf 12877 peano3nninf 12878 nninfalllemn 12879 nninfalllem1 12880 nninfself 12886 nninfsellemeq 12887 nninfsellemeqinf 12889 isomninnlem 12902 trilpolemlt1 12911 |
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