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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 4271 xpss12 4729 coss1 4777 coss2 4778 cnvss 4795 rnss 4852 ssres 4928 ssres2 4929 imass1 4998 imass2 4999 imadif 5291 imain 5293 ssoprab2 5924 suppssfv 6072 suppssov1 6073 tposss 6240 ss2ixp 6704 isumsplit 11470 isumrpcl 11473 |
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