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Mirrors > Home > NFE Home > Th. List > spfw | Unicode version |
Description: Weak version of sp 1747. Uses only Tarski's FOL axiom schemes. Lemma 9 of [KalishMontague] p. 87. This may be the best we can do with minimal distinct variable conditions. TO DO: Do we need this theorem? If not, maybe it should be deleted. (Contributed by NM, 19-Apr-2017.) |
Ref | Expression |
---|---|
spfw.1 |
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spfw.2 |
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spfw.3 |
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spfw.4 |
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Ref | Expression |
---|---|
spfw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spfw.2 |
. . 3
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2 | ax-5 1557 |
. . 3
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3 | spfw.3 |
. . . 4
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4 | spfw.4 |
. . . . . 6
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5 | 4 | biimprd 214 |
. . . . 5
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6 | 5 | equcoms 1681 |
. . . 4
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7 | 3, 6 | spimw 1668 |
. . 3
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8 | 1, 2, 7 | syl56 30 |
. 2
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9 | spfw.1 |
. . 3
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10 | 4 | biimpd 198 |
. . 3
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11 | 9, 10 | spimw 1668 |
. 2
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12 | 8, 11 | mpg 1548 |
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-17 1616 ax-9 1654 ax-8 1675 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 |
This theorem is referenced by: spnfwOLD 1692 |
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