Theorem psubnfr-P6.VR 785

Description: Variable Restricted Form of psubnfr-P6 784.

'𝑥' cannot occur in '𝜑'.

Assertion

Ref	Expression
psubnfr-P6.VR	⊢ ([𝑡 / 𝑥]𝜑 ↔ 𝜑)

Distinct variable group:   𝜑,𝑥

Proof of Theorem psubnfr-P6.VR

Step	Hyp	Ref	Expression
1		nfrv-P6 686	. 2 ⊢ Ⅎ𝑥𝜑
2	1	psubnfr-P6 784	1 ⊢ ([𝑡 / 𝑥]𝜑 ↔ 𝜑)

Syntax hints:   ↔ 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-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:  psubsplitelof-P6  801  psubvar2-P6  803  psubzero-P6  804