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Axiom ax-io 630
Description: Definition of 'or'. One of the axioms of propositional logic. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-io (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))

Detailed syntax breakdown of Axiom ax-io
StepHypRef Expression
1 wph . . . 4 wff 𝜑
2 wch . . . 4 wff 𝜒
31, 2wo 629 . . 3 wff (𝜑𝜒)
4 wps . . 3 wff 𝜓
53, 4wi 4 . 2 wff ((𝜑𝜒) → 𝜓)
61, 4wi 4 . . 3 wff (𝜑𝜓)
72, 4wi 4 . . 3 wff (𝜒𝜓)
86, 7wa 97 . 2 wff ((𝜑𝜓) ∧ (𝜒𝜓))
95, 8wb 98 1 wff (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff set class
This axiom is referenced by:  jaob  631  bj-inf2vnlem1  9942
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