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Metamath Proof Explorer

Theorem pm4.15

Description: Theorem *4.15 of WhiteheadRussell p. 117. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 18-Nov-2012)

Ref Expression
Assertion pm4.15 
|- ( ( ( ph /\ ps ) -> -. ch ) <-> ( ( ps /\ ch ) -> -. ph ) )

Proof

Step Hyp Ref Expression
1 con2b 
 |-  ( ( ( ps /\ ch ) -> -. ph ) <-> ( ph -> -. ( ps /\ ch ) ) )
2 nan 
 |-  ( ( ph -> -. ( ps /\ ch ) ) <-> ( ( ph /\ ps ) -> -. ch ) )
3 1 2 bitr2i 
 |-  ( ( ( ph /\ ps ) -> -. ch ) <-> ( ( ps /\ ch ) -> -. ph ) )