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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege63a | Structured version Visualization version GIF version |
Description: Proposition 63 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege63a | ⊢ (if-(𝜑, 𝜓, 𝜃) → (𝜂 → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege62a 40233 | . 2 ⊢ (if-(𝜑, 𝜓, 𝜃) → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏))) | |
2 | frege24 40168 | . 2 ⊢ ((if-(𝜑, 𝜓, 𝜃) → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏))) → (if-(𝜑, 𝜓, 𝜃) → (𝜂 → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (if-(𝜑, 𝜓, 𝜃) → (𝜂 → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 if-wif 1057 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-frege1 40143 ax-frege2 40144 ax-frege8 40162 ax-frege58a 40228 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ifp 1058 |
This theorem is referenced by: (None) |
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