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Metamath Proof Explorer

Theorem biimpd

Description: Deduce an implication from a logical equivalence. Deduction associated with biimp and biimpi . (Contributed by NM, 11-Jan-1993)

Ref Expression
Hypothesis biimpd.1 
|- ( ph -> ( ps <-> ch ) )
Assertion biimpd 
|- ( ph -> ( ps -> ch ) )

Proof

Step Hyp Ref Expression
1 biimpd.1 
 |-  ( ph -> ( ps <-> ch ) )
2 biimp 
 |-  ( ( ps <-> ch ) -> ( ps -> ch ) )
3 1 2 syl 
 |-  ( ph -> ( ps -> ch ) )