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Mirrors > Home > NFE Home > Th. List > an32 | GIF version |
Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995.) (Proof shortened by Wolf Lammen, 25-Dec-2012.) |
Ref | Expression |
---|---|
an32 | ⊢ (((φ ∧ ψ) ∧ χ) ↔ ((φ ∧ χ) ∧ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 630 | . 2 ⊢ (((φ ∧ ψ) ∧ χ) ↔ (φ ∧ (ψ ∧ χ))) | |
2 | an12 772 | . 2 ⊢ ((φ ∧ (ψ ∧ χ)) ↔ (ψ ∧ (φ ∧ χ))) | |
3 | ancom 437 | . 2 ⊢ ((ψ ∧ (φ ∧ χ)) ↔ ((φ ∧ χ) ∧ ψ)) | |
4 | 1, 2, 3 | 3bitri 262 | 1 ⊢ (((φ ∧ ψ) ∧ χ) ↔ ((φ ∧ χ) ∧ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∧ wa 358 |
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 177 df-an 360 |
This theorem is referenced by: an32s 779 3anan32 946 indifdir 3511 inrab2 3528 reupick 3539 resco 5085 imadif 5171 dff1o3 5292 f11o 5315 respreima 5410 dff1o6 5475 brpprod 5839 |
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