Theorem jaob 699

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 698. (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 698	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104   ∨ wo 697

This theorem was proved from axioms:  ax-io 698

This theorem is referenced by:  olc  700  orc  701  pm3.44  704  pm4.77  788  pm5.53  791  unss  3250  ralunb  3257  intun  3802  intpr  3803  relop  4689  indstr  9388  algcvgblem  11730  sqrt2irr  11840  bj-inf2vnlem1  13168