Theorem nfreetjust-P8 1115

Description: Justification Theorem for df-nfreet-D8.1 1116. †

'𝑦' and '𝑧' are distinct from all other variables.

Assertion

Ref	Expression
nfreetjust-P8	⊢ (∀𝑦Ⅎ𝑥 𝑦 = 𝑡 ↔ ∀𝑧Ⅎ𝑥 𝑧 = 𝑡)

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

Proof of Theorem nfreetjust-P8

Step	Hyp	Ref	Expression
1		ndsubeql-P7.22a.CL 911	. . 3 ⊢ (𝑦 = 𝑧 → (𝑦 = 𝑡 ↔ 𝑧 = 𝑡))
2	1	ndnfrleq-P7.11.VR 862	. 2 ⊢ (𝑦 = 𝑧 → (Ⅎ𝑥 𝑦 = 𝑡 ↔ Ⅎ𝑥 𝑧 = 𝑡))
3	2	cbvall-P7.VR12of2 1064	1 ⊢ (∀𝑦Ⅎ𝑥 𝑦 = 𝑡 ↔ ∀𝑧Ⅎ𝑥 𝑧 = 𝑡)

Syntax hints:  term-obj 1   = wff-equals 6  ∀wff-forall 8   ↔ wff-bi 104  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-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

This theorem is referenced by: (None)