Theorem ndnfrnfr-P7.12 837

Description: Natural Deduction: Effective Non-Freeness Rule 12.

The effective non-freeness predicate is itself is effectively not free. In semantic terms, this means that the effective non-freeness of the object variable '𝑥' does not depend on it's value assignment.

Assertion

Ref	Expression
ndnfrnfr-P7.12	⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Proof of Theorem ndnfrnfr-P7.12

Step	Hyp	Ref	Expression
1		nfrnfr-P6 821	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:  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-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:  nfrgencl-P7  965  dfnfreealtonlyif-P7  966