Metamath Proof Explorer


Theorem bnj290

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

Ref Expression
Assertion bnj290 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑𝜒𝜃𝜓 ) )

Proof

Step Hyp Ref Expression
1 3anrot ( ( 𝜓𝜒𝜃 ) ↔ ( 𝜒𝜃𝜓 ) )
2 1 anbi2i ( ( 𝜑 ∧ ( 𝜓𝜒𝜃 ) ) ↔ ( 𝜑 ∧ ( 𝜒𝜃𝜓 ) ) )
3 bnj252 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑 ∧ ( 𝜓𝜒𝜃 ) ) )
4 bnj252 ( ( 𝜑𝜒𝜃𝜓 ) ↔ ( 𝜑 ∧ ( 𝜒𝜃𝜓 ) ) )
5 2 3 4 3bitr4i ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑𝜒𝜃𝜓 ) )