Theorem jaob 712

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 711. (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 711	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 710

This theorem was proved from axioms:  ax-io 711

This theorem is referenced by:  olc  713  orc  714  pm3.44  717  pm4.77  801  pm5.53  804  unss  3347  ralunb  3354  intun  3916  intpr  3917  relop  4828  indstr  9714  algcvgblem  12371  sqrt2irr  12484  2sqlem6  15597  bj-inf2vnlem1  15906