Theorem jaob 715

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 714. (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 714	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 713

This theorem was proved from axioms:  ax-io 714

This theorem is referenced by:  olc  716  orc  717  pm3.44  720  pm4.77  804  pm5.53  807  unss  3378  ralunb  3385  intun  3953  intpr  3954  relop  4871  indstr  9784  algcvgblem  12566  sqrt2irr  12679  2sqlem6  15793  bj-inf2vnlem1  16291