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Mirrors > Home > MPE Home > Th. List > 3imp21 | Structured version Visualization version GIF version |
Description: The importation inference 3imp 1249 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) |
Ref | Expression |
---|---|
3imp21.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
3imp21 | ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imp21.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | 1 | 3imp 1249 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
3 | 2 | 3com12 1261 | 1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 df-3an 1033 |
This theorem is referenced by: sotri3 5445 gausslemma2dlem1a 24890 ax6e2ndeqALT 38189 fmtnofac2 40019 upgrewlkle2 40808 pthdivtx 40935 clwlksfclwwlk 41269 upgr3v3e3cycl 41347 upgr4cycl4dv4e 41352 av-extwwlkfablem2 41510 av-numclwwlkovf2ex 41517 av-frgraregord013 41549 |
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