Theorem ndnfrneg-P7.2.CL 904

Description: Closed Form of ndnfrneg-P7.2 827. †

Assertion

Ref	Expression
ndnfrneg-P7.2.CL	⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)

Proof of Theorem ndnfrneg-P7.2.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥𝜑)
2	1	ndnfrneg-P7.2 827	1 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10  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

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-nfree-D6.1 682

This theorem is referenced by:  nfrnegbi-P8  1113