Theorem ndnfrex1-P7.8 833

Description: Natural Deduction: Effective Non-Freeness Rule 8.

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

Assertion

Ref	Expression
ndnfrex1-P7.8	⊢ Ⅎ𝑥∃𝑥𝜑

Proof of Theorem ndnfrex1-P7.8

Step	Hyp	Ref	Expression
1		nfrex1-P6 742	1 ⊢ Ⅎ𝑥∃𝑥𝜑

Syntax hints:  ∃wff-exists 595  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-L10 27

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:  allnegex-P7-L1  956  allnegex-P7-L2  957  dfnfreealtif-P7  964  qimeqallhalf-P7  975  axL11ex-P7  981  exnegallint-P7  1047  qimeqex-P7-L1  1054  qimeqex-P7-L2  1055  exgennfr-P8  1085  idempotex-P8  1094  idempotallex-P8  1095  idempotexnex-P8  1098  idempotallnex-P8  1099