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Mirrors > Home > MPE Home > Th. List > an21 | Structured version Visualization version GIF version |
Description: Swap two conjuncts. (Contributed by Peter Mazsa, 18-Sep-2022.) |
Ref | Expression |
---|---|
an21 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biid 261 | . . 3 ⊢ ((𝜑 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒)) | |
2 | 1 | bianassc 643 | . 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒)) |
3 | 2 | bicomi 224 | 1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 206 ∧ wa 395 |
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 207 df-an 396 |
This theorem is referenced by: an32 646 an13 647 indifdi 4300 fncnv 6641 mpocurryd 8293 rexuz2 12939 resmndismnd 18834 imasabl 19909 logfac2 27276 ltgov 28620 brimg 35919 eldmqsres 38269 xrninxp2 38375 |
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