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Mirrors > Home > ILE Home > Th. List > 3sstr4g | Unicode version |
Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
3sstr4g.1 |
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3sstr4g.2 |
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3sstr4g.3 |
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Ref | Expression |
---|---|
3sstr4g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr4g.1 |
. 2
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2 | 3sstr4g.2 |
. . 3
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3 | 3sstr4g.3 |
. . 3
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4 | 2, 3 | sseq12i 3183 |
. 2
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5 | 1, 4 | sylibr 134 |
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: rabss2 3238 unss2 3306 sslin 3361 ssopab2 4275 xpss12 4733 coss1 4782 coss2 4783 cnvss 4800 rnss 4857 ssres 4933 ssres2 4934 imass1 5003 imass2 5004 imadif 5296 imain 5298 ssoprab2 5930 suppssfv 6078 suppssov1 6079 tposss 6246 ss2ixp 6710 isumsplit 11498 isumrpcl 11501 |
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