Theorem jaob 711

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 710. (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 710	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 709

This theorem was proved from axioms:  ax-io 710

This theorem is referenced by:  olc  712  orc  713  pm3.44  716  pm4.77  800  pm5.53  803  unss  3333  ralunb  3340  intun  3901  intpr  3902  relop  4812  indstr  9658  algcvgblem  12187  sqrt2irr  12300  2sqlem6  15207  bj-inf2vnlem1  15462