Theorem bitr2d 245

Description: Deduction form of bitr2i 241. (Contributed by NM, 9-Jun-2004.)

Hypotheses

Ref	Expression
bitr2d.1	⊢ (φ → (ψ ↔ χ))
bitr2d.2	⊢ (φ → (χ ↔ θ))

Assertion

Ref	Expression
bitr2d	⊢ (φ → (θ ↔ ψ))

Proof of Theorem bitr2d

Step	Hyp	Ref	Expression
1		bitr2d.1	. . 3 ⊢ (φ → (ψ ↔ χ))
2		bitr2d.2	. . 3 ⊢ (φ → (χ ↔ θ))
3	1, 2	bitrd 244	. 2 ⊢ (φ → (ψ ↔ θ))
4	3	bicomd 192	1 ⊢ (φ → (θ ↔ ψ))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  3bitrrd  271  3bitr2rd  273  pm5.18  345  fnasrn  5418