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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 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))

Proof of Theorem pm2.04
StepHypRef Expression
1 id 22 . 2 ((𝜑 → (𝜓𝜒)) → (𝜑 → (𝜓𝜒)))
21com23 86 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  91  com45  97  bi2.04  376  merco2  1658  ralcom3  3100  bj-exalim  32245  syl5imp  38186  com3rgbi  38188  syl5impVD  38568  simplbi2comtVD  38593  19.41rgVD  38607  ax6e2eqVD  38612  rexrsb  40460
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