Theorem joinimandinc3-P4.RC 579

Description: Inference Form of joinimandinc3-P4 578. †

Hypotheses

Ref	Expression
joinimandinc3-P4.RC.1	⊢ (𝜑 → 𝜓)
joinimandinc3-P4.RC.2	⊢ (𝜒 → 𝜓)

Assertion

Ref	Expression
joinimandinc3-P4.RC	⊢ ((𝜑 ∨ 𝜒) → 𝜓)

Proof of Theorem joinimandinc3-P4.RC

Step	Hyp	Ref	Expression
1		joinimandinc3-P4.RC.1	. . . 4 ⊢ (𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜓))
3		joinimandinc3-P4.RC.2	. . . 4 ⊢ (𝜒 → 𝜓)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜒 → 𝜓))
5	2, 4	joinimandinc3-P4 578	. 2 ⊢ (⊤ → ((𝜑 ∨ 𝜒) → 𝜓))
6	5	ndtruee-P3.18 183	1 ⊢ ((𝜑 ∨ 𝜒) → 𝜓)

Syntax hints:   → wff-imp 10   ∨ 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:  qimeqallhalf-P5  609  qimeqex-P5-L1  610  psubim-P6-L2  790