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Mirrors > Home > ILE Home > Th. List > ax9o | Unicode version |
Description: An implication related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
ax9o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1674 | . 2 | |
2 | 19.29r 1600 | . . 3 | |
3 | hba1 1520 | . . . . 5 | |
4 | pm3.35 344 | . . . . 5 | |
5 | 3, 4 | exlimih 1572 | . . . 4 |
6 | ax-4 1487 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | 2, 7 | syl 14 | . 2 |
9 | 1, 8 | mpan 420 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wceq 1331 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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: equsalh 1704 spimth 1713 spimh 1715 |
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