Theorem ndnfrneg-P7.2.RC 875

Description: Inference Form of ndnfrneg-P7.2 827.

Hypothesis

Ref	Expression
ndnfrneg-P7.2.RC.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
ndnfrneg-P7.2.RC	⊢ Ⅎ𝑥 ¬ 𝜑

Proof of Theorem ndnfrneg-P7.2.RC

Step	Hyp	Ref	Expression
1		ndnfrneg-P7.2.RC.1	. . . 4 ⊢ Ⅎ𝑥𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
3	2	ndnfrneg-P7.2 827	. 2 ⊢ (⊤ → Ⅎ𝑥 ¬ 𝜑)
4	3	ndtruee-P3.18 183	1 ⊢ Ⅎ𝑥 ¬ 𝜑

Syntax hints:  ¬ wff-neg 9  ⊤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

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:  allnegex-P7-L2  957  axL10-P7  979  qimeqex-P7-L1  1054  idempotallnall-P8  1097  idempotexnex-P8  1098  idempotallnex-P8  1099  idempotexnall-P8  1100