Theorem bitr2d 407

Description: Deduction form of bitr2 152.

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 406	. 2 ⊢ (φ → (ψ ↔ θ))
4	3	bicomd 399	1 ⊢ (φ → (θ ↔ ψ))

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  ltdivmult 4408  nnleltp1t 4448  nn0ltlem1 4558  nn0subt 4587  znnsubt 4595  zlem1ltt 4599  uzind 4603  sqrle 4765  znnen 4930  elat2 5739

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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