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Mirrors > Home > ILE Home > Th. List > 3sstr4i | Unicode version |
Description: Substitution of equality in both sides of a subclass relationship. (Contributed by NM, 13-Jan-1996.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
3sstr4.1 |
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3sstr4.2 |
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3sstr4.3 |
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Ref | Expression |
---|---|
3sstr4i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr4.1 |
. 2
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2 | 3sstr4.2 |
. . 3
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3 | 3sstr4.3 |
. . 3
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4 | 2, 3 | sseq12i 2965 |
. 2
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5 | 1, 4 | mpbir 134 |
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: undif2ss 3293 pwsnss 3565 iinuniss 3728 brab2a 4336 rncoss 4545 imassrn 4622 rnin 4676 inimass 4683 imadiflem 4921 imainlem 4923 ssoprab2i 5535 npsspw 6454 axresscn 6746 |
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