New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > breq1 | Unicode version |
Description: Equality theorem for a binary relation. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
breq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1 4578 | . . 3 | |
2 | 1 | eleq1d 2419 | . 2 |
3 | df-br 4640 | . 2 | |
4 | df-br 4640 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 279 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wcel 1710 cop 4561 class class class wbr 4639 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-addc 4378 df-nnc 4379 df-phi 4565 df-op 4566 df-br 4640 |
This theorem is referenced by: breq12 4644 breq1i 4646 breq1d 4649 nbrne2 4657 brab1 4684 vtoclr 4816 brco 4883 brcnv 4892 dfdmf 4905 elimapw1 4944 dfrnf 4962 dfres2 5002 imasn 5018 coi1 5094 dffun6f 5123 funmo 5125 fun11 5159 fneu 5187 fveq2 5328 nfunsn 5353 dmfco 5381 dff13 5471 isorel 5489 isocnv 5491 isotr 5495 isomin 5496 isoini 5497 f1oiso 5499 f1oiso2 5500 funsi 5520 caovord 5629 caovord3 5631 brsnsi 5773 brsnsi1 5775 brco1st 5777 brco2nd 5778 trtxp 5781 elfix 5787 op1st2nd 5790 brimage 5793 txpcofun 5803 otsnelsi3 5805 addcfnex 5824 qrpprod 5836 brpprod 5839 dmpprod 5840 fnpprod 5843 clos1ex 5876 clos1conn 5879 clos1basesuc 5882 trd 5921 symd 5924 antid 5929 connexd 5931 weds 5938 en0 6042 fndmeng 6046 endisj 6051 xpassenlem 6056 xpassen 6057 enpw1 6062 enmap2 6068 enpw1pw 6075 nenpw1pwlem2 6085 enpw 6087 lecex 6115 ovmuc 6130 mucnc 6131 mucex 6133 ncdisjun 6136 ceexlem1 6173 ceex 6174 elce 6175 ltlenlec 6207 leltctr 6212 leconnnc 6218 lenc 6223 ce2le 6233 ce0lenc1 6239 tcfnex 6244 nclenn 6249 csucex 6259 addccan2nclem1 6263 ncslesuc 6267 nmembers1lem1 6268 nmembers1lem3 6270 nncdiv3lem1 6275 nncdiv3lem2 6276 nnc3n3p1 6278 spacvallem1 6281 nchoicelem11 6299 nchoicelem16 6304 nchoicelem19 6307 fnfreclem3 6319 fnfrec 6320 frecsuc 6322 |
Copyright terms: Public domain | W3C validator |