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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege19 | Structured version Visualization version GIF version |
Description: A closed form of syl6 35. Proposition 19 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege19 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜒 → 𝜃) → (𝜑 → (𝜓 → 𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege9 42172 | . 2 ⊢ ((𝜓 → 𝜒) → ((𝜒 → 𝜃) → (𝜓 → 𝜃))) | |
2 | frege18 42178 | . 2 ⊢ (((𝜓 → 𝜒) → ((𝜒 → 𝜃) → (𝜓 → 𝜃))) → ((𝜑 → (𝜓 → 𝜒)) → ((𝜒 → 𝜃) → (𝜑 → (𝜓 → 𝜃))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜒 → 𝜃) → (𝜑 → (𝜓 → 𝜃)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42150 ax-frege2 42151 ax-frege8 42169 |
This theorem is referenced by: frege21 42187 frege20 42188 frege71 42294 frege86 42309 frege103 42326 frege119 42342 frege123 42346 |
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