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Mirrors > Home > ILE Home > Th. List > anandirs | GIF version |
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.) |
Ref | Expression |
---|---|
anandirs.1 | ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜓 ∧ 𝜒)) → 𝜏) |
Ref | Expression |
---|---|
anandirs | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anandirs.1 | . . 3 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜓 ∧ 𝜒)) → 𝜏) | |
2 | 1 | an4s 552 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜒)) → 𝜏) |
3 | 2 | anabsan2 548 | 1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 |
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 |
This theorem is referenced by: 3impdir 1225 fvreseq 5292 phplem4 6341 muladd 7488 iccshftr 9016 iccshftl 9018 iccdil 9020 icccntr 9022 fzaddel 9077 fzsubel 9078 mulexp 9515 |
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