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Axiom ax-io 607
Description: Definition of 'or'. Axiom 6 of 10 for intuitionistic logic.
Assertion
Ref Expression
ax-io (((φ χ) → ψ) ↔ ((φψ) (χψ)))

Detailed syntax breakdown of Axiom ax-io
StepHypRef Expression
1 wph . . . 4 wff φ
2 wch . . . 4 wff χ
31, 2wo 606 . . 3 wff (φ χ)
4 wps . . 3 wff ψ
53, 4wi 4 . 2 wff ((φ χ) → ψ)
61, 4wi 4 . . 3 wff (φψ)
72, 4wi 4 . . 3 wff (χψ)
86, 7wa 96 . 2 wff ((φψ) (χψ))
95, 8wb 97 1 wff (((φ χ) → ψ) ↔ ((φψ) (χψ)))
Colors of variables: wff set class
This axiom is referenced by:  jaob  608
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