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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  392  merco2  1738  ralcom3  3355  bj-exalim  34025  syl5imp  41142  com3rgbi  41144  syl5impVD  41493  simplbi2comtVD  41518  19.41rgVD  41532  ax6e2eqVD  41537  adh-jarrsc  43523  adh-minim  43524  adh-minimp  43536  rexrsb  43585
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