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Mirrors > Home > ILE Home > Th. List > 3comr | GIF version |
Description: Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.) |
Ref | Expression |
---|---|
3exp.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3comr | ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exp.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3coml 1189 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃) |
3 | 2 | 3coml 1189 | 1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 965 |
This theorem is referenced by: nnacan 6416 le2tri3i 7896 ltaddsublt 8357 div12ap 8478 lemul12b 8643 zdivadd 9164 zdivmul 9165 elfz 9827 fzmmmeqm 9869 fzrev 9895 absdiflt 10896 absdifle 10897 dvds0lem 11539 dvdsmulc 11557 dvds2add 11563 dvds2sub 11564 dvdstr 11566 lcmdvds 11796 psmettri2 12536 xmettri2 12569 |
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