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Mirrors > Home > MPE Home > Th. List > anabsi8 | Structured version Visualization version GIF version |
Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999.) |
Ref | Expression |
---|---|
anabsi8.1 | ⊢ (𝜓 → ((𝜓 ∧ 𝜑) → 𝜒)) |
Ref | Expression |
---|---|
anabsi8 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabsi8.1 | . . 3 ⊢ (𝜓 → ((𝜓 ∧ 𝜑) → 𝜒)) | |
2 | 1 | anabsi5 666 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
3 | 2 | ancoms 459 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
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 206 df-an 397 |
This theorem is referenced by: subuhgr 27641 subupgr 27642 subumgr 27643 subusgr 27644 |
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