Theorem sepimandr-P4.9a.CL 408

Description: Closed Form of sepimandr-P4.9a 406. †

Assertion

Ref	Expression
sepimandr-P4.9a.CL	⊢ ((𝜑 → (𝜓 ∧ 𝜒)) → ((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)))

Proof of Theorem sepimandr-P4.9a.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ ((𝜑 → (𝜓 ∧ 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒)))
2	1	sepimandr-P4.9a 406	1 ⊢ ((𝜑 → (𝜓 ∧ 𝜒)) → ((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)))

Syntax hints:   → wff-imp 10   ∧ wff-and 132

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-true-D2.4 155

This theorem is referenced by:  imoverand-P4.29a  472