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Mirrors > Home > ILE Home > Th. List > 3impdi | GIF version |
Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.) |
Ref | Expression |
---|---|
3impdi.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜃) |
Ref | Expression |
---|---|
3impdi | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3impdi.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜃) | |
2 | 1 | anandis 556 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
3 | 2 | 3impb 1134 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: ecovdi 6240 ecovidi 6241 distrpig 6523 mulcanenq 6575 mulcanenq0ec 6635 distrnq0 6649 axltadd 7182 absmulgcd 10406 |
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