Description: If Y belongs to the R -sequence beginning with Z , then every result of an application of the procedure R to Y belongs to the R -sequence beginning with Z . Proposition 108 of Frege1879 p. 74. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)
Ref | Expression | ||
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Hypotheses | frege108.z | |- Z e. A |
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frege108.y | |- Y e. B |
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frege108.v | |- V e. C |
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frege108.r | |- R e. D |
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Assertion | frege108 | |- ( Z ( ( t+ ` R ) u. _I ) Y -> ( Y R V -> Z ( ( t+ ` R ) u. _I ) V ) ) |
Step | Hyp | Ref | Expression |
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1 | frege108.z | |- Z e. A |
|
2 | frege108.y | |- Y e. B |
|
3 | frege108.v | |- V e. C |
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4 | frege108.r | |- R e. D |
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5 | 1 2 3 4 | frege102 | |- ( Z ( ( t+ ` R ) u. _I ) Y -> ( Y R V -> Z ( t+ ` R ) V ) ) |
6 | 3 | frege107 | |- ( ( Z ( ( t+ ` R ) u. _I ) Y -> ( Y R V -> Z ( t+ ` R ) V ) ) -> ( Z ( ( t+ ` R ) u. _I ) Y -> ( Y R V -> Z ( ( t+ ` R ) u. _I ) V ) ) ) |
7 | 5 6 | ax-mp | |- ( Z ( ( t+ ` R ) u. _I ) Y -> ( Y R V -> Z ( ( t+ ` R ) u. _I ) V ) ) |