Theorem sepimorl-P4.9b.RC 410

Description: Inference Form of sepimorl-P4.9b 409. †

Hypothesis

Ref	Expression
sepimorl-P4.9b.RC.1	⊢ ((𝜑 ∨ 𝜓) → 𝜒)

Assertion

Ref	Expression
sepimorl-P4.9b.RC	⊢ ((𝜑 → 𝜒) ∧ (𝜓 → 𝜒))

Proof of Theorem sepimorl-P4.9b.RC

Step	Hyp	Ref	Expression
1		sepimorl-P4.9b.RC.1	. . . 4 ⊢ ((𝜑 ∨ 𝜓) → 𝜒)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ((𝜑 ∨ 𝜓) → 𝜒))
3	2	sepimorl-P4.9b 409	. 2 ⊢ (⊤ → ((𝜑 → 𝜒) ∧ (𝜓 → 𝜒)))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜑 → 𝜒) ∧ (𝜓 → 𝜒))

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

This theorem is referenced by: (None)