Theorem trujust 1404

Description: Soundness justification theorem for df-tru 1405. (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 174	1 |- ( ( A. x x = x -> A. x x = x ) <-> ( A. y y = y -> A. y y = y ) )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105   A.wal 1400   = wceq 1402

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by: (None)