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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege24 | Structured version Visualization version GIF version |
Description: Closed form for a1d 25. Deduction introducing an embedded antecedent. Identical to rp-frege24 42548 which was proved without relying on ax-frege8 42560. Proposition 24 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege24 | ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege1 42541 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜒 → (𝜑 → 𝜓))) | |
2 | frege12 42564 | . 2 ⊢ (((𝜑 → 𝜓) → (𝜒 → (𝜑 → 𝜓))) → ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42541 ax-frege2 42542 ax-frege8 42560 |
This theorem is referenced by: frege25 42568 frege63a 42632 frege63b 42659 frege63c 42677 |
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