Theorem jaob 669

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 668. (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 668	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104   ∨ wo 667

This theorem was proved from axioms:  ax-io 668

This theorem is referenced by:  olc  670  orc  671  pm3.44  673  pm4.77  751  pm5.53  754  unss  3189  ralunb  3196  intun  3741  intpr  3742  relop  4617  indstr  9180  algcvgblem  11458  sqrt2irr  11568  bj-inf2vnlem1  12573