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| Mirrors > Home > MPE Home > Th. List > ax-1 | Structured version Visualization version GIF version | ||
| Description: Axiom Simp. Axiom A1 of [Margaris] p. 49. One of the 3 axioms of propositional calculus. The 3 axioms are also given as Definition 2.1 of [Hamilton] p. 28. This axiom is called Simp or "the principle of simplification" in Principia Mathematica (Theorem *2.02 of [WhiteheadRussell] p. 100) because "it enables us to pass from the joint assertion of 𝜑 and 𝜓 to the assertion of 𝜑 simply". It is Proposition 1 of [Frege1879] p. 26, its first axiom. (Contributed by NM, 30-Sep-1992.) |
| Ref | Expression |
|---|---|
| ax-1 | ⊢ (𝜑 → (𝜓 → 𝜑)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph | . 2 wff 𝜑 | |
| 2 | wps | . . 3 wff 𝜓 | |
| 3 | 2, 1 | wi 4 | . 2 wff (𝜓 → 𝜑) |
| 4 | 1, 3 | wi 4 | 1 wff (𝜑 → (𝜓 → 𝜑)) |
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