This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3bitr3g

Description: More general version of 3bitr3i . Useful for converting definitions in a formula. (Contributed by NM, 4-Jun-1995)

Ref Expression
Hypotheses 3bitr3g.1 ⊢ φ → ψ ↔ χ
3bitr3g.2 ⊢ ψ ↔ θ
3bitr3g.3 ⊢ χ ↔ τ
Assertion 3bitr3g ⊢ φ → θ ↔ τ

Proof

Step Hyp Ref Expression
1 3bitr3g.1 ⊢ φ → ψ ↔ χ
2 3bitr3g.2 ⊢ ψ ↔ θ
3 3bitr3g.3 ⊢ χ ↔ τ
4 2 1 bitr3id ⊢ φ → θ ↔ χ
5 4 3 bitrdi ⊢ φ → θ ↔ τ