Theorem oroverand-P4.27b 464

Description: '∨' Distributes Over '∧'. †

Assertion

Ref	Expression
oroverand-P4.27b	⊢ ((𝜑 ∨ (𝜓 ∧ 𝜒)) ↔ ((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ 𝜒)))

Proof of Theorem oroverand-P4.27b

Step	Hyp	Ref	Expression
1		oroverand-P4.27-L3 462	. 2 ⊢ ((𝜑 ∨ (𝜓 ∧ 𝜒)) → ((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ 𝜒)))
2		oroverand-P4.27-L4 463	. 2 ⊢ (((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ 𝜒)) → (𝜑 ∨ (𝜓 ∧ 𝜒)))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 ∨ (𝜓 ∧ 𝜒)) ↔ ((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ 𝜒)))

Syntax hints:   ↔ wff-bi 104   ∧ wff-and 132   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-rcp-AND4 163

This theorem is referenced by:  oroverbi-P4.28-L3  468