Theorem jaob 710

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 709. (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 709	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 708

This theorem was proved from axioms:  ax-io 709

This theorem is referenced by:  olc  711  orc  712  pm3.44  715  pm4.77  799  pm5.53  802  unss  3309  ralunb  3316  intun  3875  intpr  3876  relop  4777  indstr  9591  algcvgblem  12043  sqrt2irr  12156  2sqlem6  14349  bj-inf2vnlem1  14604