This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm5.501

Description: Theorem *5.501 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm5.501 
|- ( ph -> ( ps <-> ( ph <-> ps ) ) )

Proof

Step Hyp Ref Expression
1 pm5.1im 
 |-  ( ph -> ( ps -> ( ph <-> ps ) ) )
2 biimp 
 |-  ( ( ph <-> ps ) -> ( ph -> ps ) )
3 2 com12 
 |-  ( ph -> ( ( ph <-> ps ) -> ps ) )
4 1 3 impbid 
 |-  ( ph -> ( ps <-> ( ph <-> ps ) ) )