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Mirrors > Home > ILE Home > Th. List > ax-in2 | GIF version |
Description: 'Not' elimination. One of the axioms of propositional logic. (Contributed by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
ax-in2 | ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | 1 | wn 3 | . 2 wff ¬ 𝜑 |
3 | wps | . . 3 wff 𝜓 | |
4 | 1, 3 | wi 4 | . 2 wff (𝜑 → 𝜓) |
5 | 2, 4 | wi 4 | 1 wff (¬ 𝜑 → (𝜑 → 𝜓)) |
Colors of variables: wff set class |
This axiom is referenced by: pm2.21 612 con2d 619 imorr 716 dcim 836 condcOLD 849 pm5.14dc 906 pm5.54dc 913 mon 2048 difin 3364 indifdir 3383 sosng 4684 iotanul 5175 |
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