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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 2965 |
. 2
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5 | 1, 4 | sylibr 137 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-in 2918 df-ss 2925 |
This theorem is referenced by: rabss2 3017 unss2 3108 sslin 3157 ssopab2 4003 xpss12 4388 coss1 4434 coss2 4435 cnvss 4451 rnss 4507 ssres 4580 ssres2 4581 imass1 4643 imass2 4644 imadif 4922 imain 4924 ssoprab2 5503 suppssfv 5650 suppssov1 5651 tposss 5802 |
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