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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 2183 |
. 2
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3 | eqsstrrd.2 |
. 2
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4 | 2, 3 | eqsstrd 3191 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 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-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 |
This theorem is referenced by: ssxpbm 5059 ssxp1 5060 ssxp2 5061 suppssof1 6093 tfrlemiubacc 6324 tfr1onlemubacc 6340 tfrcllemubacc 6353 oaword1 6465 phplem4dom 6855 fisseneq 6924 nnnninfeq2 7120 archnqq 7394 ringidss 13025 epttop 13223 metequiv2 13629 limccnpcntop 13777 limccnp2lem 13778 limccnp2cntop 13779 nnsf 14377 |
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