Theorem tbt

Description: A wff is equivalent to its equivalence with a truth. (Contributed by NM, 18-Aug-1993) (Proof shortened by Andrew Salmon, 13-May-2011)

	Ref	Expression
Hypothesis	tbt.1	⊢ 𝜑
Assertion	tbt	⊢ ( 𝜓 ↔ ( 𝜓 ↔ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		tbt.1	⊢ 𝜑
2		ibibr	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → ( 𝜓 ↔ 𝜑 ) ) )
3	2	pm5.74ri	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜓 ↔ 𝜑 ) ) )
4	1 3	ax-mp	⊢ ( 𝜓 ↔ ( 𝜓 ↔ 𝜑 ) )