Theorem jaob 722

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 721. (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 721	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 720

This proof depends on axioms:  ax-io 721

This theorem is used by:  olc  723  orc  724  pm3.44  727  pm4.77  811  pm5.53  814  unss  3403  ralunb  3410  intun  4001  intpr  4002  relop  4930  indstr  9993  algcvgblem  12827  sqrt2irr  12940  2sqlem6  16239  bj-inf2vnlem1  16996