Theorem jaob 705

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 704. (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 704	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104   ∨ wo 703

This theorem was proved from axioms:  ax-io 704

This theorem is referenced by:  olc  706  orc  707  pm3.44  710  pm4.77  794  pm5.53  797  unss  3301  ralunb  3308  intun  3862  intpr  3863  relop  4761  indstr  9552  algcvgblem  12003  sqrt2irr  12116  2sqlem6  13750  bj-inf2vnlem1  14005