Metamath Proof Explorer


Theorem 3bitr4g

Description: More general version of 3bitr4i . Useful for converting definitions in a formula. (Contributed by NM, 11-May-1993)

Ref Expression
Hypotheses 3bitr4g.1 ( 𝜑 → ( 𝜓𝜒 ) )
3bitr4g.2 ( 𝜃𝜓 )
3bitr4g.3 ( 𝜏𝜒 )
Assertion 3bitr4g ( 𝜑 → ( 𝜃𝜏 ) )

Proof

Step Hyp Ref Expression
1 3bitr4g.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 3bitr4g.2 ( 𝜃𝜓 )
3 3bitr4g.3 ( 𝜏𝜒 )
4 2 1 syl5bb ( 𝜑 → ( 𝜃𝜒 ) )
5 4 3 bitr4di ( 𝜑 → ( 𝜃𝜏 ) )