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Mirrors > Home > ILE Home > Th. List > 3sstr4d | Unicode version |
Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 30-Nov-1995.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
3sstr4d.1 |
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3sstr4d.2 |
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3sstr4d.3 |
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Ref | Expression |
---|---|
3sstr4d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr4d.1 |
. 2
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2 | 3sstr4d.2 |
. . 3
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3 | 3sstr4d.3 |
. . 3
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4 | 2, 3 | sseq12d 3188 |
. 2
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5 | 1, 4 | mpbird 167 |
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 3137 df-ss 3144 |
This theorem is referenced by: rdgss 6386 sucinc2 6449 oawordi 6472 nnnninf 7126 fzoss1 10173 fzoss2 10174 clsss 13657 ntrss 13658 sslm 13786 txss12 13805 metss2lem 14036 xmettxlem 14048 xmettx 14049 nnsf 14793 nninfself 14801 |
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