Metamath Proof Explorer


Theorem pm2.04

Description: Swap antecedents. Theorem *2.04 of WhiteheadRussell p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of Frege1879 p. 35. Its associated inference is com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 12-Sep-2012)

Ref Expression
Assertion pm2.04
|- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )

Proof

Step Hyp Ref Expression
1 id
 |-  ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
2 1 com23
 |-  ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )