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Mirrors > Home > MPE Home > Th. List > pm2.04 | Structured version Visualization version GIF version |
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 84 | 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 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 |
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