Theorem jaob 717

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 716. (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 716	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 715

This theorem was proved from axioms:  ax-io 716

This theorem is referenced by:  olc  718  orc  719  pm3.44  722  pm4.77  806  pm5.53  809  unss  3381  ralunb  3388  intun  3959  intpr  3960  relop  4880  indstr  9826  algcvgblem  12620  sqrt2irr  12733  2sqlem6  15848  bj-inf2vnlem1  16565