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Mirrors > Home > MPE Home > Th. List > bianass | Structured version Visualization version GIF version |
Description: An inference to merge two lists of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019.) |
Ref | Expression |
---|---|
bianass.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) |
Ref | Expression |
---|---|
bianass | ⊢ ((𝜂 ∧ 𝜑) ↔ ((𝜂 ∧ 𝜓) ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bianass.1 | . . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) | |
2 | 1 | anbi2i 626 | . 2 ⊢ ((𝜂 ∧ 𝜑) ↔ (𝜂 ∧ (𝜓 ∧ 𝜒))) |
3 | anass 472 | . 2 ⊢ (((𝜂 ∧ 𝜓) ∧ 𝜒) ↔ (𝜂 ∧ (𝜓 ∧ 𝜒))) | |
4 | 2, 3 | bitr4i 281 | 1 ⊢ ((𝜂 ∧ 𝜑) ↔ ((𝜂 ∧ 𝜓) ∧ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∧ 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: bianassc 643 an12 645 an4 656 cnvresima 6072 elcncf1di 23660 nb3grpr2 27338 wwlksnextwrd 27848 cusgr3cyclex 32682 satfvsuclem2 32906 bj-prmoore 34940 bj-imdirco 35015 redundpim3 36399 isthincd2 45840 |
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