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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-frege2 | Structured version Visualization version Unicode version |
Description: If a proposition is a necessary consequence of two propositions and and one of those, , is in turn a necessary consequence of the other, , then the proposition is a necessary consequence of the latter one, , alone. Axiom 2 of [Frege1879] p. 26. Identical to ax-2 7. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-frege2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . 2 | |
2 | wps | . . 3 | |
3 | wch | . . 3 | |
4 | 2, 3 | wi 4 | . 2 |
5 | 1, 3 | wi 4 | . . 3 |
6 | 1, 2, 5 | bj-0 32533 | . 2 |
7 | 1, 4, 6 | bj-0 32533 | 1 |
Colors of variables: wff setvar class |
This axiom is referenced by: rp-frege3g 38088 frege3 38089 rp-misc1-frege 38090 rp-frege24 38091 rp-frege4g 38092 frege4 38093 rp-7frege 38095 rp-8frege 38098 frege39 38136 frege73 38230 frege79 38236 |
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