Theorem rimoverand-P4.31a 481

Description: '→' is Antidistributive on the Right Over '∧'.

Assertion

Ref	Expression
rimoverand-P4.31a	⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜑 → 𝜒) ∨ (𝜓 → 𝜒)))

Proof of Theorem rimoverand-P4.31a

Step	Hyp	Ref	Expression
1		sepimandl-P4.9d.CL 417	. 2 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) → ((𝜑 → 𝜒) ∨ (𝜓 → 𝜒)))
2		rimoverand-P4.31-L1 480	. 2 ⊢ (((𝜑 → 𝜒) ∨ (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒))
3	1, 2	rcp-NDBII0 239	1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜑 → 𝜒) ∨ (𝜓 → 𝜒)))

Syntax hints:   → wff-imp 10   ↔ 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

This theorem is referenced by: (None)