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Mirrors > Home > ILE Home > Th. List > eqsstrrd | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.) |
Ref | Expression |
---|---|
eqsstrrd.1 |
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eqsstrrd.2 |
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Ref | Expression |
---|---|
eqsstrrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqsstrrd.1 |
. . 3
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2 | 1 | eqcomd 2146 |
. 2
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3 | eqsstrrd.2 |
. 2
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4 | 2, 3 | eqsstrd 3138 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 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-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-in 3082 df-ss 3089 |
This theorem is referenced by: ssxpbm 4982 ssxp1 4983 ssxp2 4984 suppssof1 6007 tfrlemiubacc 6235 tfr1onlemubacc 6251 tfrcllemubacc 6264 oaword1 6375 phplem4dom 6764 fisseneq 6828 archnqq 7249 epttop 12298 metequiv2 12704 limccnpcntop 12852 limccnp2lem 12853 limccnp2cntop 12854 nnsf 13374 |
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