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Mirrors > Home > ILE Home > Th. List > spime | Unicode version |
Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Mar-2018.) |
Ref | Expression |
---|---|
spime.1 |
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spime.2 |
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Ref | Expression |
---|---|
spime |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spime.1 |
. . . 4
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2 | 1 | a1i 9 |
. . 3
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3 | spime.2 |
. . 3
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4 | 2, 3 | spimed 1686 |
. 2
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5 | 4 | mptru 1308 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-4 1455 ax-i9 1478 ax-ial 1482 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 |
This theorem is referenced by: spimev 1800 |
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