Theorem trujust 1397

Description: Soundness justification theorem for df-tru 1398. (Contributed by Mario Carneiro, 17-Nov-2013.) (Revised by NM, 11-Jul-2019.)

Assertion

Ref	Expression
trujust	No typesetting for: |- ( ( A. x x = x -> A. x x = x ) <-> ( A. y y = y -> A. y y = y ) )

Proof of Theorem trujust

Step	Hyp	Ref	Expression
1		id 22	. 2 No typesetting for: |- ( A. x x = x -> A. x x = x )
2		id 22	. 2 No typesetting for: |- ( A. y y = y -> A. y y = y )
3	1, 2	2th 239	1 No typesetting for: |- ( ( A. x x = x -> A. x x = x ) <-> ( A. y y = y -> A. y y = y ) )

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185