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Mirrors > Home > ILE Home > Th. List > ax-io | GIF version |
Description: Definition of 'or'. Axiom 6 of 10 for intuitionistic logic. (Contributed by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
ax-io | ⊢ (((φ ∨ χ) → ψ) ↔ ((φ → ψ) ∧ (χ → ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . . 4 wff φ | |
2 | wch | . . . 4 wff χ | |
3 | 1, 2 | wo 628 | . . 3 wff (φ ∨ χ) |
4 | wps | . . 3 wff ψ | |
5 | 3, 4 | wi 4 | . 2 wff ((φ ∨ χ) → ψ) |
6 | 1, 4 | wi 4 | . . 3 wff (φ → ψ) |
7 | 2, 4 | wi 4 | . . 3 wff (χ → ψ) |
8 | 6, 7 | wa 97 | . 2 wff ((φ → ψ) ∧ (χ → ψ)) |
9 | 5, 8 | wb 98 | 1 wff (((φ ∨ χ) → ψ) ↔ ((φ → ψ) ∧ (χ → ψ))) |
Colors of variables: wff set class |
This axiom is referenced by: jaob 630 bj-inf2vnlem1 9430 |
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