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Mirrors > Home > ILE Home > Th. List > equsex | Unicode version |
Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
equsex.1 | |
equsex.2 |
Ref | Expression |
---|---|
equsex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsex.1 | . . 3 | |
2 | equsex.2 | . . . 4 | |
3 | 2 | biimpa 294 | . . 3 |
4 | 1, 3 | exlimih 1557 | . 2 |
5 | a9e 1659 | . . 3 | |
6 | idd 21 | . . . . 5 | |
7 | 2 | biimprcd 159 | . . . . 5 |
8 | 6, 7 | jcad 305 | . . . 4 |
9 | 1, 8 | eximdh 1575 | . . 3 |
10 | 5, 9 | mpi 15 | . 2 |
11 | 4, 10 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-i9 1495 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: cbvexh 1713 sb56 1841 cleljust 1890 sb10f 1948 |
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