Theorem trujust 1318

Description: Soundness justification theorem for df-tru 1319. (Contributed by Mario Carneiro, 17-Nov-2013.)

Assertion

Ref	Expression
trujust	⊢ ((φ ↔ φ) ↔ (ψ ↔ ψ))

Proof of Theorem trujust

Step	Hyp	Ref	Expression
1		biid 227	. 2 ⊢ (φ ↔ φ)
2		biid 227	. 2 ⊢ (ψ ↔ ψ)
3	1, 2	2th 230	1 ⊢ ((φ ↔ φ) ↔ (ψ ↔ ψ))

Syntax hints:   ↔ wb 176

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 177

This theorem is referenced by: (None)