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| 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.) | 
| Ref | Expression | 
|---|---|
| pm2.04 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒))) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → 𝜒))) | |
| 2 | 1 | com23 86 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒))) | 
| 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 bi2.04 387 merco2 1736 ralcom3OLD 3098 spcimgft 3546 bj-exalim 36633 syl5imp 44532 com3rgbi 44534 syl5impVD 44883 simplbi2comtVD 44908 19.41rgVD 44922 ax6e2eqVD 44927 adh-jarrsc 47012 adh-minim 47013 adh-minimp 47025 rexrsb 47112 | 
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