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Mirrors > Home > ILE Home > Th. List > exdistrfor | Unicode version |
Description: Distribution of existential quantifiers, with a bound-variable hypothesis saying that is not free in , but can be free in (and there is no distinct variable condition on and ). (Contributed by Jim Kingdon, 25-Feb-2018.) |
Ref | Expression |
---|---|
exdistrfor.1 |
Ref | Expression |
---|---|
exdistrfor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exdistrfor.1 | . 2 | |
2 | biidd 171 | . . . . . 6 | |
3 | 2 | drex1 1770 | . . . . 5 |
4 | 3 | drex2 1710 | . . . 4 |
5 | hbe1 1471 | . . . . . 6 | |
6 | 5 | 19.9h 1622 | . . . . 5 |
7 | 19.8a 1569 | . . . . . . 7 | |
8 | 7 | anim2i 339 | . . . . . 6 |
9 | 8 | eximi 1579 | . . . . 5 |
10 | 6, 9 | sylbi 120 | . . . 4 |
11 | 4, 10 | syl6bir 163 | . . 3 |
12 | ax-ial 1514 | . . . 4 | |
13 | 19.40 1610 | . . . . . 6 | |
14 | 19.9t 1621 | . . . . . . . 8 | |
15 | 14 | biimpd 143 | . . . . . . 7 |
16 | 15 | anim1d 334 | . . . . . 6 |
17 | 13, 16 | syl5 32 | . . . . 5 |
18 | 17 | sps 1517 | . . . 4 |
19 | 12, 18 | eximdh 1590 | . . 3 |
20 | 11, 19 | jaoi 705 | . 2 |
21 | 1, 20 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 697 wal 1329 wnf 1436 wex 1468 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 |
This theorem is referenced by: oprabidlem 5795 |
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