Metamath Proof Explorer


Theorem an42

Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996)

Ref Expression
Assertion an42 ( ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) ↔ ( ( 𝜑𝜒 ) ∧ ( 𝜃𝜓 ) ) )

Proof

Step Hyp Ref Expression
1 an4 ( ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) ↔ ( ( 𝜑𝜒 ) ∧ ( 𝜓𝜃 ) ) )
2 ancom ( ( 𝜓𝜃 ) ↔ ( 𝜃𝜓 ) )
3 2 anbi2i ( ( ( 𝜑𝜒 ) ∧ ( 𝜓𝜃 ) ) ↔ ( ( 𝜑𝜒 ) ∧ ( 𝜃𝜓 ) ) )
4 1 3 bitri ( ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) ↔ ( ( 𝜑𝜒 ) ∧ ( 𝜃𝜓 ) ) )