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Mirrors > Home > ILE Home > Th. List > ax10oe | Unicode version |
Description: Quantifier Substitution
for existential quantifiers. Analogue to ax10o 1725
but for ![]() ![]() |
Ref | Expression |
---|---|
ax10oe |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-ia3 108 |
. . . 4
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2 | 1 | alimi 1465 |
. . 3
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3 | exim 1609 |
. . 3
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4 | 2, 3 | syl 14 |
. 2
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5 | ax11e 1806 |
. . 3
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6 | 5 | sps 1547 |
. 2
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7 | 4, 6 | syld 45 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-11 1516 ax-4 1520 ax-ial 1544 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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