Theorem tbt 236

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

Hypothesis

Ref	Expression
tbt.1	⊢ φ

Assertion

Ref	Expression
tbt	⊢ (ψ ↔ (ψ ↔ φ))

Proof of Theorem tbt

Step	Hyp	Ref	Expression
1		tbt.1	. 2 ⊢ φ
2		ibibr 235	. . 3 ⊢ ((φ → ψ) ↔ (φ → (ψ ↔ φ)))
3	2	pm5.74ri 170	. 2 ⊢ (φ → (ψ ↔ (ψ ↔ φ)))
4	1, 3	ax-mp 7	1 ⊢ (ψ ↔ (ψ ↔ φ))

Syntax hints:   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  tbtru  1238  exists1  1978  reu6  2707  eqv  3217  vprc  3862  bj-vprc  7119