Theorem bj-dvelimv 32836

Description: A version of dvelim 2337 using the "non-free" idiom. (Contributed by BJ, 20-Oct-2021.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bj-dvelimv.nf	|- F/ x ps
bj-dvelimv.is	|- ( z = y -> ( ps <-> ph ) )

Assertion

Ref	Expression
bj-dvelimv	|- ( -. A. x x = y -> F/ x ph )

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

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

Proof of Theorem bj-dvelimv

Step	Hyp	Ref	Expression
1		nfv 1843	. . 3 |- F/ x T.
2		bj-dvelimv.nf	. . . 4 |- F/ x ps
3	2	a1i 11	. . 3 |- ( T. -> F/ x ps )
4		bj-dvelimv.is	. . 3 |- ( z = y -> ( ps <-> ph ) )
5	1, 3, 4	bj-dvelimdv1 32835	. 2 |- ( T. -> ( -. A. x x = y -> F/ x ph ) )
6	5	trud 1493	1 |- ( -. A. x x = y -> F/ x ph )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   A.wal 1481   T. wtru 1484   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:  bj-nfeel2  32837