Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > an3 | Structured version Visualization version GIF version |
Description: A rearrangement of conjuncts. (Contributed by Rodolfo Medina, 25-Sep-2010.) |
Ref | Expression |
---|---|
an3 | ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜑 ∧ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an43 658 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ↔ ((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜒))) | |
2 | 1 | simplbi 501 | 1 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜑 ∧ 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: catideu 17049 usgredg2v 27169 prtlem15 36512 clsk1indlem3 41199 poprelb 44510 |
Copyright terms: Public domain | W3C validator |