Theorem nfrnegbi-P8 1113

Description: Biconditional Combining ndnfrneg-P7.2 827 and nfrnegconv-P8 1110.

This statement is not deducible with intuitionist logic.

Assertion

Ref	Expression
nfrnegbi-P8	⊢ (Ⅎ𝑥 ¬ 𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem nfrnegbi-P8

Step	Hyp	Ref	Expression
1		nfrnegconv-P8.CL 1112	. 2 ⊢ (Ⅎ𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑)
2		ndnfrneg-P7.2.CL 904	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
3	1, 2	rcp-NDBII0 239	1 ⊢ (Ⅎ𝑥 ¬ 𝜑 ↔ Ⅎ𝑥𝜑)

Syntax hints:  ¬ wff-neg 9   ↔ wff-bi 104  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-false-D2.5 158  df-rcp-AND3 161  df-exists-D5.1 596  df-nfree-D6.1 682  df-psub-D6.2 716

This theorem is referenced by: (None)