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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege21 | Structured version Visualization version GIF version |
Description: Replace antecedent in antecedent. Proposition 21 of [Frege1879] p. 40. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege21 | ⊢ (((𝜑 → 𝜓) → 𝜒) → ((𝜑 → 𝜃) → ((𝜃 → 𝜓) → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege9 41402 | . 2 ⊢ ((𝜑 → 𝜃) → ((𝜃 → 𝜓) → (𝜑 → 𝜓))) | |
2 | frege19 41414 | . 2 ⊢ (((𝜑 → 𝜃) → ((𝜃 → 𝜓) → (𝜑 → 𝜓))) → (((𝜑 → 𝜓) → 𝜒) → ((𝜑 → 𝜃) → ((𝜃 → 𝜓) → 𝜒)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (((𝜑 → 𝜓) → 𝜒) → ((𝜑 → 𝜃) → ((𝜃 → 𝜓) → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 41380 ax-frege2 41381 ax-frege8 41399 |
This theorem is referenced by: frege44 41438 frege47 41441 |
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