Theorem alloverim-P5.RC 589

Description: Inference Form of alloverim-P5 588.

Hypothesis

Ref	Expression
alloverim-P5.RC.1	⊢ ∀𝑥(𝜑 → 𝜓)

Assertion

Ref	Expression
alloverim-P5.RC	⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem alloverim-P5.RC

Step	Hyp	Ref	Expression
1		alloverim-P5.RC.1	. . . 4 ⊢ ∀𝑥(𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ∀𝑥(𝜑 → 𝜓))
3	2	alloverim-P5 588	. 2 ⊢ (⊤ → (∀𝑥𝜑 → ∀𝑥𝜓))
4	3	ndtruee-P3.18 183	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:  ∀wff-forall 8   → wff-imp 10  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-L4 16

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by:  alloverim-P5.RC.GEN  592  suballinf-P5  594