Metamath Proof Explorer


Theorem anbi1ci

Description: Variant of anbi1i with commutation. (Contributed by Peter Mazsa, 7-Mar-2020)

Ref Expression
Hypothesis anbi.1 ( 𝜑𝜓 )
Assertion anbi1ci ( ( 𝜒𝜑 ) ↔ ( 𝜓𝜒 ) )

Proof

Step Hyp Ref Expression
1 anbi.1 ( 𝜑𝜓 )
2 1 anbi2i ( ( 𝜒𝜑 ) ↔ ( 𝜒𝜓 ) )
3 2 biancomi ( ( 𝜒𝜑 ) ↔ ( 𝜓𝜒 ) )