Metamath Proof Explorer


Theorem anbi2i

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)

Ref Expression
Hypothesis anbi.1 ( 𝜑𝜓 )
Assertion anbi2i ( ( 𝜒𝜑 ) ↔ ( 𝜒𝜓 ) )

Proof

Step Hyp Ref Expression
1 anbi.1 ( 𝜑𝜓 )
2 1 a1i ( 𝜒 → ( 𝜑𝜓 ) )
3 2 pm5.32i ( ( 𝜒𝜑 ) ↔ ( 𝜒𝜓 ) )