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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-frege1 | Structured version Visualization version GIF version |
Description: The case in which 𝜑 is denied, 𝜓 is affirmed, and 𝜑 is affirmed is excluded. This is evident since 𝜑 cannot at the same time be denied and affirmed. Axiom 1 of [Frege1879] p. 26. Identical to ax-1 6. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-frege1 | ⊢ (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)) |
Colors of variables: wff setvar class |
This axiom is referenced by: rp-simp2-frege 40493 rp-frege3g 40495 frege3 40496 frege5 40501 rp-6frege 40504 frege26 40511 frege27 40512 frege11 40515 frege24 40516 frege36 40540 |
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