Theorem alloverim-P5.RC.GEN 592

Description: Inference Form of alloverim-P5 588 with Generalization.

For the deductive form with a variable restriction see alloverim-P5.GENV 621. For the most general form, see alloverim-P5.GENF 747.

Hypothesis

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

Assertion

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

Proof of Theorem alloverim-P5.RC.GEN

Step	Hyp	Ref	Expression
1		alloverim-P5.RC.GEN.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	ax-GEN 15	. 2 ⊢ ∀𝑥(𝜑 → 𝜓)
3	2	alloverim-P5.RC 589	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:  ∀wff-forall 8   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  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:  qimeqallhalf-P5  609  allicv-P5  614  cbvallv-P5-L1  658  lemma-L5.04a  667  nfrall2w-P6  694  specpsub-P6  721  nfrall2-P6  743  allic-P6  745  exgennfrcl-L6  814