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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 2695 | . . 3 | |
2 | nfa1 1521 | . . . 4 | |
3 | ceqsalg.1 | . . . 4 | |
4 | ceqsalg.2 | . . . . . . 7 | |
5 | 4 | biimpd 143 | . . . . . 6 |
6 | 5 | a2i 11 | . . . . 5 |
7 | 6 | sps 1517 | . . . 4 |
8 | 2, 3, 7 | exlimd 1576 | . . 3 |
9 | 1, 8 | syl5com 29 | . 2 |
10 | 4 | biimprcd 159 | . . 3 |
11 | 3, 10 | alrimi 1502 | . 2 |
12 | 9, 11 | impbid1 141 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wnf 1436 wex 1468 wcel 1480 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: ceqsal 2710 sbc6g 2928 uniiunlem 3180 sucprcreg 4459 funimass4 5465 ralrnmpo 5878 |
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