Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.04 Structured version   Visualization version   GIF version

Theorem pm2.04 88
 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 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))

Proof of Theorem pm2.04
StepHypRef Expression
1 id 22 . 2 ((𝜑 → (𝜓𝜒)) → (𝜑 → (𝜓𝜒)))
21com23 84 1 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
 Colors of variables: wff setvar class 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  89  com45  95  bi2.04  375  merco2  1652  ralcom3  3084  syl5imp  37739  com3rgbi  37741  syl5impVD  38121  simplbi2comtVD  38146  19.41rgVD  38160  ax6e2eqVD  38165  rexrsb  39818
 Copyright terms: Public domain W3C validator