Metamath Proof Explorer


Theorem 3anan32OLD

Description: Obsolete version of 3anan32 as of 15-Jun-2026. Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Assertion 3anan32OLD ( ( 𝜑𝜓𝜒 ) ↔ ( ( 𝜑𝜒 ) ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 df-3an ( ( 𝜑𝜓𝜒 ) ↔ ( ( 𝜑𝜓 ) ∧ 𝜒 ) )
2 an32 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ↔ ( ( 𝜑𝜒 ) ∧ 𝜓 ) )
3 1 2 bitri ( ( 𝜑𝜓𝜒 ) ↔ ( ( 𝜑𝜒 ) ∧ 𝜓 ) )