Theorem jaob 700

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 699. (Contributed by NM, 30-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
jaob	⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Proof of Theorem jaob

Step	Hyp	Ref	Expression
1		ax-io 699	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104   ∨ wo 698

This theorem was proved from axioms:  ax-io 699

This theorem is referenced by:  olc  701  orc  702  pm3.44  705  pm4.77  789  pm5.53  792  unss  3255  ralunb  3262  intun  3810  intpr  3811  relop  4697  indstr  9415  algcvgblem  11766  sqrt2irr  11876  bj-inf2vnlem1  13339