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Mirrors > Home > ILE Home > Th. List > sseqtrd | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.) |
Ref | Expression |
---|---|
sseqtrd.1 |
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sseqtrd.2 |
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Ref | Expression |
---|---|
sseqtrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtrd.1 |
. 2
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2 | sseqtrd.2 |
. . 3
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3 | 2 | sseq2d 3037 |
. 2
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4 | 1, 3 | mpbid 145 |
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 104 ax-ia2 105 ax-ia3 106 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-11 1438 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-in 2989 df-ss 2996 |
This theorem is referenced by: sseqtr4d 3046 resasplitss 5121 nnaword2 6175 erssxp 6217 phpm 6422 ioodisj 9127 |
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