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Mirrors > Home > ILE Home > Th. List > anandis | GIF version |
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.) |
Ref | Expression |
---|---|
anandis.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜏) |
Ref | Expression |
---|---|
anandis | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anandis.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜏) | |
2 | 1 | an4s 556 | . 2 ⊢ (((𝜑 ∧ 𝜑) ∧ (𝜓 ∧ 𝜒)) → 𝜏) |
3 | 2 | anabsan 543 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: 3impdi 1236 dff13 5585 f1oiso 5643 ltapig 6994 ltmpig 6995 faclbnd 10280 tgcl 11932 |
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