Theorem nfrvar-P8 1118

Description: Any variable '𝑥' is ENF in term consisting of some variable, '𝑦', that is different from '𝑥'. †

Assertion

Ref	Expression
nfrvar-P8	⊢ Ⅎt𝑥 𝑦

Distinct variable group:   𝑥,𝑦

Proof of Theorem nfrvar-P8

Dummy variable 𝑧 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. . 3 ⊢ Ⅎ𝑥 𝑧 = 𝑦
2	1	axGEN-P7 933	. 2 ⊢ ∀𝑧Ⅎ𝑥 𝑧 = 𝑦
3		df-nfreet-D8.1 1116	. 2 ⊢ (Ⅎt𝑥 𝑦 ↔ ∀𝑧Ⅎ𝑥 𝑧 = 𝑦)
4	2, 3	bimpr-P4.RC 534	1 ⊢ Ⅎt𝑥 𝑦

Syntax hints:  term-obj 1   = wff-equals 6  ∀wff-forall 8  Ⅎwff-nfree 681  Ⅎ_twff-nfreet 1114

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-L11 28  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  df-nfreet-D8.1 1116

This theorem is referenced by: (None)