Theorem bj-vtocl 32909

Description: Remove dependency on ax-ext 2602, df-clab 2609 and df-cleq 2615 (and df-sb 1881 and df-v 3202) from vtocl 3259. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bj-vtocl.s	|- A e. V
bj-vtocl.maj	|- ( x = A -> ( ph <-> ps ) )
bj-vtocl.min	|- ph

Assertion

Ref	Expression
bj-vtocl	|- ps

Distinct variable groups:   x, A   ps, x   x, V

Allowed substitution hint:   ph( x)

Proof of Theorem bj-vtocl

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x ps
2		bj-vtocl.s	. 2 |- A e. V
3		bj-vtocl.maj	. 2 |- ( x = A -> ( ph <-> ps ) )
4		bj-vtocl.min	. 2 |- ph
5	1, 2, 3, 4	bj-vtoclf 32908	1 |- ps

Syntax hints:   -> wi 4   <-> wb 196   = wceq 1483   e. wcel 1990

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-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710  df-clel 2618

This theorem is referenced by: (None)