Theorem ndpsub3-P7.15 840

Description: Natural Deduction: Proper Substitution Rule 3.

'𝑥' cannot occur in '𝑡'.

Assertion

Ref	Expression
ndpsub3-P7.15	⊢ Ⅎ𝑥[𝑡 / 𝑥]𝜑

Distinct variable group:   𝑡,𝑥

Proof of Theorem ndpsub3-P7.15

Step	Hyp	Ref	Expression
1		lemma-L6.06a 766	1 ⊢ Ⅎ𝑥[𝑡 / 𝑥]𝜑

Syntax hints:  Ⅎwff-nfree 681  [wff-psub 714

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  df-psub-D6.2 716

This theorem is referenced by:  psubnfrv-P7  927  psubinv-P7  939  lemma-L7.02a-L1  943  lemma-L7.03  962  dfpsubv-P7  977  cbvallpsub-P7  1070  cbvexpsub-P7  1072