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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 3058 |
. 2
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5 | 1, 4 | mpbird 166 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3008 df-ss 3015 |
This theorem is referenced by: rdgss 6164 sucinc2 6223 oawordi 6246 nnnninf 6869 fzoss1 9645 fzoss2 9646 clsss 11881 ntrss 11882 nnsf 12198 nninfself 12208 |
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