Theorem ndpsub4-P7.16 841

Description: Natural Deduction: Proper Substitution Rule 4.

'𝑥' can occur in '𝑡', but '𝑦' cannot occur in either '𝜑' or '𝑡'.

Assertion

Ref	Expression
ndpsub4-P7.16	⊢ ([𝑡 / 𝑥]𝜑 ↔ [𝑡 / 𝑦][𝑦 / 𝑥]𝜑)

Distinct variable groups:   𝜑,𝑦   𝑡,𝑦   𝑥,𝑦

Proof of Theorem ndpsub4-P7.16

Step	Hyp	Ref	Expression
1		psubcomp-P6 767	1 ⊢ ([𝑡 / 𝑥]𝜑 ↔ [𝑡 / 𝑦][𝑦 / 𝑥]𝜑)

Syntax hints:  term-obj 1   ↔ wff-bi 104  [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:  psubid-P7  940  lemma-L7.02a  944  dfpsub-P7  978