Theorem ndnfrall2-P7.9.RC 880

Description: Inference Form of ndnfrall2-P7.9 834.

Hypothesis

Ref	Expression
ndnfrall2-P7.9.RC.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
ndnfrall2-P7.9.RC	⊢ Ⅎ𝑥∀𝑦𝜑

Distinct variable group:   𝑥,𝑦

Proof of Theorem ndnfrall2-P7.9.RC

Step	Hyp	Ref	Expression
1		ndnfrall2-P7.9.RC.1	. . . 4 ⊢ Ⅎ𝑥𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
3	2	ndnfrall2-P7.9.VR12of2 860	. 2 ⊢ (⊤ → Ⅎ𝑥∀𝑦𝜑)
4	3	ndtruee-P3.18 183	1 ⊢ Ⅎ𝑥∀𝑦𝜑

Syntax hints:  ∀wff-forall 8  ⊤wff-true 153  Ⅎwff-nfree 681

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17  ax-L6 18  ax-L7 19  ax-L10 27  ax-L11 28  ax-L12 29

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  df-exists-D5.1 596  df-nfree-D6.1 682

This theorem is referenced by:  axL11-P7  980  cbvall-P7-L1  1060