Theorem jaob 718

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 717. (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 717	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 716

This theorem was proved from axioms:  ax-io 717

This theorem is referenced by:  olc  719  orc  720  pm3.44  723  pm4.77  807  pm5.53  810  unss  3383  ralunb  3390  intun  3964  intpr  3965  relop  4886  indstr  9888  algcvgblem  12701  sqrt2irr  12814  2sqlem6  15939  bj-inf2vnlem1  16686