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Mirrors > Home > ILE Home > Th. List > eqsstrri | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.) |
Ref | Expression |
---|---|
eqsstr3.1 | |
eqsstr3.2 |
Ref | Expression |
---|---|
eqsstrri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqsstr3.1 | . . 3 | |
2 | 1 | eqcomi 2174 | . 2 |
3 | eqsstr3.2 | . 2 | |
4 | 2, 3 | eqsstri 3179 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wss 3121 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-in 3127 df-ss 3134 |
This theorem is referenced by: inss2 3348 dmv 4825 resasplitss 5375 ofrfval 6067 ofvalg 6068 ofrval 6069 off 6071 ofres 6073 ofco 6077 dftpos4 6240 smores2 6271 caseinj 7063 djuinj 7080 bcm1k 10683 bcpasc 10689 |
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