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Mirrors > Home > ILE Home > Th. List > dmeq | Unicode version |
Description: Equality theorem for domain. (Contributed by NM, 11-Aug-1994.) |
Ref | Expression |
---|---|
dmeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmss 4746 |
. . 3
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2 | dmss 4746 |
. . 3
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3 | 1, 2 | anim12i 336 |
. 2
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4 | eqss 3117 |
. 2
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5 | eqss 3117 |
. 2
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6 | 3, 4, 5 | 3imtr4i 200 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-dm 4557 |
This theorem is referenced by: dmeqi 4748 dmeqd 4749 xpid11 4770 sqxpeq0 4970 fneq1 5219 eqfnfv2 5527 offval 5997 ofrfval 5998 offval3 6040 smoeq 6195 tfrlemi14d 6238 tfr1onlemres 6254 tfrcllemres 6267 rdgivallem 6286 rdgon 6291 rdg0 6292 frec0g 6302 freccllem 6307 frecfcllem 6309 frecsuclem 6311 frecsuc 6312 ereq1 6444 fundmeng 6709 acfun 7080 ccfunen 7096 ennnfonelemj0 11950 ennnfonelemg 11952 ennnfonelemp1 11955 ennnfonelemom 11957 ennnfonelemnn0 11971 blfvalps 12593 reldvg 12856 |
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