Theorem joinimor-P4.8c.CL 405

Description: Closed Form of joinimor-P4.8c 403. †

Assertion

Ref	Expression
joinimor-P4.8c.CL	⊢ (((𝜑 → 𝜓) ∨ (𝜒 → 𝜗)) → ((𝜑 ∧ 𝜒) → (𝜓 ∨ 𝜗)))

Proof of Theorem joinimor-P4.8c.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (((𝜑 → 𝜓) ∨ (𝜒 → 𝜗)) → ((𝜑 → 𝜓) ∨ (𝜒 → 𝜗)))
2	1	joinimor-P4.8c 403	1 ⊢ (((𝜑 → 𝜓) ∨ (𝜒 → 𝜗)) → ((𝜑 ∧ 𝜒) → (𝜓 ∨ 𝜗)))

Syntax hints:   → wff-imp 10   ∧ 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:  imoveror-P4.29-L1  473  rimoverand-P4.31-L1  480