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Mirrors > Home > ILE Home > Th. List > ax10oe | Unicode version |
Description: Quantifier Substitution for existential quantifiers. Analogue to ax10o 1695 but for rather than . (Contributed by Jim Kingdon, 21-Dec-2017.) |
Ref | Expression |
---|---|
ax10oe |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-ia3 107 | . . . 4 | |
2 | 1 | alimi 1435 | . . 3 |
3 | exim 1579 | . . 3 | |
4 | 2, 3 | syl 14 | . 2 |
5 | ax11e 1776 | . . 3 | |
6 | 5 | sps 1517 | . 2 |
7 | 4, 6 | syld 45 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1333 wceq 1335 wex 1472 |
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 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-11 1486 ax-4 1490 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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