Theorem jaob 631

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. (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 630	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98   ∨ wo 629

This theorem was proved from axioms:  ax-io 630

This theorem is referenced by:  olc  632  orc  633  pm3.44  635  pm4.77  712  pm5.53  715  unss  3117  ralunb  3124  intun  3646  intpr  3647  relop  4486  indstr  8536  sqrt2irr  9878  algcvgblem  9888