Metamath Proof Explorer


Theorem bnj170

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj170 ( ( 𝜑𝜓𝜒 ) ↔ ( ( 𝜓𝜒 ) ∧ 𝜑 ) )

Proof

Step Hyp Ref Expression
1 3anrot ( ( 𝜑𝜓𝜒 ) ↔ ( 𝜓𝜒𝜑 ) )
2 df-3an ( ( 𝜓𝜒𝜑 ) ↔ ( ( 𝜓𝜒 ) ∧ 𝜑 ) )
3 1 2 bitri ( ( 𝜑𝜓𝜒 ) ↔ ( ( 𝜓𝜒 ) ∧ 𝜑 ) )