Theorem joinimandinc-P4.8a.CL 399

Description: Closed Form of joinimandinc-P4.8a 397. †

Assertion

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

Proof of Theorem joinimandinc-P4.8a.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜗)) → ((𝜑 → 𝜓) ∧ (𝜒 → 𝜗)))
2	1	joinimandinc-P4.8a 397	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:  rimoveror-P4.31b  482