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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 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 bi2.04 392 merco2 1738 ralcom3 3317 bj-exalim 34078 syl5imp 41218 com3rgbi 41220 syl5impVD 41569 simplbi2comtVD 41594 19.41rgVD 41608 ax6e2eqVD 41613 adh-jarrsc 43593 adh-minim 43594 adh-minimp 43606 rexrsb 43655 |
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