Metamath Proof Explorer


Theorem impbid21d

Description: Deduce an equivalence from two implications. (Contributed by Wolf Lammen, 12-May-2013)

Ref Expression
Hypotheses impbid21d.1 ( 𝜓 → ( 𝜒𝜃 ) )
impbid21d.2 ( 𝜑 → ( 𝜃𝜒 ) )
Assertion impbid21d ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 impbid21d.1 ( 𝜓 → ( 𝜒𝜃 ) )
2 impbid21d.2 ( 𝜑 → ( 𝜃𝜒 ) )
3 impbi ( ( 𝜒𝜃 ) → ( ( 𝜃𝜒 ) → ( 𝜒𝜃 ) ) )
4 1 2 3 syl2imc ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )