Theorem joinimandinc-P4.8a.RC 398

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

Hypothesis

Ref	Expression
joinimandinc-P4.8a.RC.1	⊢ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜗))

Assertion

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

Proof of Theorem joinimandinc-P4.8a.RC

Step	Hyp	Ref	Expression
1		joinimandinc-P4.8a.RC.1	. . . 4 ⊢ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜗))
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ((𝜑 → 𝜓) ∧ (𝜒 → 𝜗)))
3	2	joinimandinc-P4.8a 397	. 2 ⊢ (⊤ → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜗)))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜗))

Syntax hints:   → wff-imp 10   ∧ wff-and 132   ∨ wff-or 144  ⊤wff-true 153

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)