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Mirrors > Home > MPE Home > Th. List > anabsi6 | Structured version Visualization version GIF version |
Description: Absorption of antecedent into conjunction. (Contributed by NM, 14-Aug-2000.) |
Ref | Expression |
---|---|
anabsi6.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜑) → 𝜒)) |
Ref | Expression |
---|---|
anabsi6 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabsi6.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜑) → 𝜒)) | |
2 | 1 | ancomsd 466 | . 2 ⊢ (𝜑 → ((𝜑 ∧ 𝜓) → 𝜒)) |
3 | 2 | anabsi5 666 | 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: anabsi7 668 pjnormssi 30518 funressndmafv2rn 44675 |
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