Theorem bj-nfeel2 32837

Description: Non-freeness in an equality. (Contributed by BJ, 20-Oct-2021.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-nfeel2	|- ( -. A. x x = y -> F/ x y e. z )

Distinct variable group:   x, z

Proof of Theorem bj-nfeel2

Dummy variable t is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x t e. z
2		elequ1 1997	. 2 |- ( t = y -> ( t e. z <-> y e. z ) )
3	1, 2	bj-dvelimv 32836	1 |- ( -. A. x x = y -> F/ x y e. z )

Syntax hints:   -. wn 3   -> wi 4   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-8 1992  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-axc14nf  32838