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 → ( 𝜓𝜒 ) )
3bitr3g.2 ( 𝜓𝜃 )
3bitr3g.3 ( 𝜒𝜏 )
Assertion 3bitr3g ( 𝜑 → ( 𝜃𝜏 ) )

Proof

Step Hyp Ref Expression
1 3bitr3g.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 3bitr3g.2 ( 𝜓𝜃 )
3 3bitr3g.3 ( 𝜒𝜏 )
4 2 1 bitr3id ( 𝜑 → ( 𝜃𝜒 ) )
5 4 3 bitrdi ( 𝜑 → ( 𝜃𝜏 ) )