Theorem ndalli-P7.17.VR1of2 864

Description: ndalli-P7.17 842 with one variable restriction. †

'𝑦' cannot occur in '𝛾'.

Hypotheses

Ref	Expression
ndalli-P7.17.VR1of2.1	⊢ Ⅎ𝑦𝜑
ndalli-P7.17.VR1of2.2	⊢ (𝛾 → [𝑦 / 𝑥]𝜑)

Assertion

Ref	Expression
ndalli-P7.17.VR1of2	⊢ (𝛾 → ∀𝑥𝜑)

Distinct variable groups:   𝛾,𝑦   𝑥,𝑦

Proof of Theorem ndalli-P7.17.VR1of2

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. 2 ⊢ Ⅎ𝑦𝛾
2		ndalli-P7.17.VR1of2.1	. 2 ⊢ Ⅎ𝑦𝜑
3		ndalli-P7.17.VR1of2.2	. 2 ⊢ (𝛾 → [𝑦 / 𝑥]𝜑)
4	1, 2, 3	ndalli-P7.17 842	1 ⊢ (𝛾 → ∀𝑥𝜑)

Syntax hints:  term-obj 1  ∀wff-forall 8   → wff-imp 10  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-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:  ndalli-P7.17.RC  883