Theorem dvelimnf 2017

Description: Version of dvelim 2016 using "not free" notation. (Contributed by Mario Carneiro, 9-Oct-2016.)

Hypotheses

Ref	Expression
dvelimnf.1	⊢ Ⅎxφ
dvelimnf.2	⊢ (z = y → (φ ↔ ψ))

Assertion

Ref	Expression
dvelimnf	⊢ (¬ ∀x x = y → Ⅎxψ)

Distinct variable group:   ψ,z

Allowed substitution hints:   φ(x,y,z)   ψ(x,y)

Proof of Theorem dvelimnf

Step	Hyp	Ref	Expression
1		dvelimnf.1	. 2 ⊢ Ⅎxφ
2		nfv 1619	. 2 ⊢ Ⅎzψ
3		dvelimnf.2	. 2 ⊢ (z = y → (φ ↔ ψ))
4	1, 2, 3	dvelimf 1997	1 ⊢ (¬ ∀x x = y → Ⅎxψ)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  nfrab  2792