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Mirrors > Home > ILE Home > Th. List > dmeqi | Unicode version |
Description: Equality inference for domain. (Contributed by NM, 4-Mar-2004.) |
Ref | Expression |
---|---|
dmeqi.1 |
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Ref | Expression |
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dmeqi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmeqi.1 |
. 2
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2 | dmeq 4823 |
. 2
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3 | 1, 2 | ax-mp 5 |
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 3597 df-pr 3598 df-op 3600 df-br 4001 df-dm 4633 |
This theorem is referenced by: dmxpm 4843 dmxpid 4844 dmxpin 4845 rncoss 4893 rncoeq 4896 rnun 5033 rnin 5034 rnxpm 5054 rnxpss 5056 imainrect 5070 dmpropg 5097 dmtpop 5100 rnsnopg 5103 fntpg 5268 fnreseql 5622 dmoprab 5950 reldmmpo 5980 elmpocl 6063 tfrlem8 6313 tfr2a 6316 tfrlemi14d 6328 tfr1onlemres 6344 tfri1dALT 6346 tfrcllemres 6357 xpassen 6824 sbthlemi5 6954 casedm 7079 djudm 7098 ctssdccl 7104 dmaddpi 7315 dmmulpi 7316 dmaddpq 7369 dmmulpq 7370 axaddf 7858 axmulf 7859 ennnfonelemom 12392 ennnfonelemdm 12404 |
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