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Mirrors > Home > ILE Home > Th. List > ceqsalg | Unicode version |
Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 29-Oct-2003.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
ceqsalg.1 | |
ceqsalg.2 |
Ref | Expression |
---|---|
ceqsalg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2735 | . . 3 | |
2 | nfa1 1528 | . . . 4 | |
3 | ceqsalg.1 | . . . 4 | |
4 | ceqsalg.2 | . . . . . . 7 | |
5 | 4 | biimpd 143 | . . . . . 6 |
6 | 5 | a2i 11 | . . . . 5 |
7 | 6 | sps 1524 | . . . 4 |
8 | 2, 3, 7 | exlimd 1584 | . . 3 |
9 | 1, 8 | syl5com 29 | . 2 |
10 | 4 | biimprcd 159 | . . 3 |
11 | 3, 10 | alrimi 1509 | . 2 |
12 | 9, 11 | impbid1 141 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wceq 1342 wnf 1447 wex 1479 wcel 2135 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2723 |
This theorem is referenced by: ceqsal 2750 sbc6g 2970 uniiunlem 3226 sucprcreg 4520 funimass4 5531 ralrnmpo 5947 |
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