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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege61a | Structured version Visualization version GIF version |
Description: Lemma for frege65a 37197. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege61a | ⊢ ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓 ∧ 𝜒) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege58a 37189 | . 2 ⊢ ((𝜓 ∧ 𝜒) → if-(𝜑, 𝜓, 𝜒)) | |
2 | frege9 37126 | . 2 ⊢ (((𝜓 ∧ 𝜒) → if-(𝜑, 𝜓, 𝜒)) → ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓 ∧ 𝜒) → 𝜃))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓 ∧ 𝜒) → 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 if-wif 1006 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 37104 ax-frege2 37105 ax-frege8 37123 ax-frege58a 37189 |
This theorem is referenced by: frege65a 37197 |
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