Theorem dvelimnf 2339

Description: Version of dvelim 2337 using "not free" notation. (Contributed by Mario Carneiro, 9-Oct-2016.)

Hypotheses

Ref	Expression
dvelimnf.1	|- F/ x ph
dvelimnf.2	|- ( z = y -> ( ph <-> ps ) )

Assertion

Ref	Expression
dvelimnf	|- ( -. A. x x = y -> F/ x ps )

Distinct variable group:   ps, z

Allowed substitution hints:   ph( x, y, z)   ps( x, y)

Proof of Theorem dvelimnf

Step	Hyp	Ref	Expression
1		dvelimnf.1	. 2 |- F/ x ph
2		nfv 1843	. 2 |- F/ z ps
3		dvelimnf.2	. 2 |- ( z = y -> ( ph <-> ps ) )
4	1, 2, 3	dvelimf 2334	1 |- ( -. A. x x = y -> F/ x ps )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   A.wal 1481   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  nfrab  3123