Theorem jaob 663

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 662. (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 662	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 102   ↔ wb 103   ∨ wo 661

This theorem was proved from axioms:  ax-io 662

This theorem is referenced by:  olc  664  orc  665  pm3.44  667  pm4.77  745  pm5.53  748  unss  3146  ralunb  3153  intun  3667  intpr  3668  relop  4504  indstr  8681  algcvgblem  10431  sqrt2irr  10541  bj-inf2vnlem1  10765