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Mirrors > Home > NFE Home > Th. List > spimeh | Unicode version |
Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Proof shortened by Wolf Lammen, 10-Dec-2017.) |
Ref | Expression |
---|---|
spimeh.1 |
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spimeh.2 |
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Ref | Expression |
---|---|
spimeh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spimeh.1 |
. 2
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2 | a9ev 1656 |
. . . 4
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3 | spimeh.2 |
. . . . 5
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4 | 3 | eximi 1576 |
. . . 4
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5 | 2, 4 | ax-mp 5 |
. . 3
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6 | 5 | 19.35i 1601 |
. 2
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7 | 1, 6 | syl 15 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-9 1654 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 |
This theorem is referenced by: ax12olem1 1927 ax10lem2 1937 |
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