Theorem trujust 1345

Description: Soundness justification theorem for df-tru 1346. (Contributed by Mario Carneiro, 17-Nov-2013.) (Revised by NM, 11-Jul-2019.)

Assertion

Ref	Expression
trujust	|- ( ( 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 19	. 2 |- ( A. x x = x -> A. x x = x )
2		id 19	. 2 |- ( A. y y = y -> A. y y = y )
3	1, 2	2th 173	1 |- ( ( A. x x = x -> A. x x = x ) <-> ( A. y y = y -> A. y y = y ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1341   = wceq 1343

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)