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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege53aid | Structured version Visualization version GIF version |
Description: Specialization of frege53a 43187. Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege53aid | ⊢ (𝜑 → ((𝜑 ↔ 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege52aid 43185 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓)) | |
2 | ax-frege8 43136 | . 2 ⊢ (((𝜑 ↔ 𝜓) → (𝜑 → 𝜓)) → (𝜑 → ((𝜑 ↔ 𝜓) → 𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → ((𝜑 ↔ 𝜓) → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-frege8 43136 ax-frege52a 43184 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-ifp 1060 df-tru 1536 df-fal 1546 |
This theorem is referenced by: (None) |
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