Metamath Proof Explorer


Theorem simplbi

Description: Deduction eliminating a conjunct. (Contributed by NM, 27-May-1998)

Ref Expression
Hypothesis simplbi.1 ( 𝜑 ↔ ( 𝜓𝜒 ) )
Assertion simplbi ( 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 simplbi.1 ( 𝜑 ↔ ( 𝜓𝜒 ) )
2 1 biimpi ( 𝜑 → ( 𝜓𝜒 ) )
3 2 simpld ( 𝜑𝜓 )