Theorem pm2.04 90

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 32. (Contributed by NM, 27-Dec-1992.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)

Assertion

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

Proof of Theorem pm2.04

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
2	1	com23 86	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  com34  91  com45  97  bi2.04  376  merco2  1661  ralcom3  3105  bj-exalim  32611  syl5imp  38718  com3rgbi  38720  syl5impVD  39099  simplbi2comtVD  39124  19.41rgVD  39138  ax6e2eqVD  39143  rexrsb  41169