Theorem ndnfrall1-P7.7 832

Description: Natural Deduction: Effective Non-Freeness Rule 7.

'𝑥' is effectively not free in '∀𝑥𝜑' (since any '𝑥' appearing '𝜑' will be bound).

Assertion

Ref	Expression
ndnfrall1-P7.7	⊢ Ⅎ𝑥∀𝑥𝜑

Proof of Theorem ndnfrall1-P7.7

Step	Hyp	Ref	Expression
1		nfrall1-P6 741	1 ⊢ Ⅎ𝑥∀𝑥𝜑

Syntax hints:  ∀wff-forall 8  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:  axL4-P7  945  axL4ex-P7  946  allnegex-P7-L1  956  gennfrcl-P7  963  dfnfreealtif-P7  964  dfnfreealtonlyif-P7  966  qimeqallhalf-P7  975  axL10-P7  979  axL11-P7  980  exnegallint-P7  1047  qimeqex-P7-L1  1054  qimeqex-P7-L2  1055  gennfr-P8  1079  idempotall-P8  1093  idempotexall-P8  1096  idempotallnall-P8  1097  idempotexnall-P8  1100