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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 577 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜒)) → 𝜏) |
3 | 2 | anabsan2 573 | 1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: 3impdir 1272 fvreseq 5517 phplem4 6742 muladd 8139 iccshftr 9770 iccshftl 9772 iccdil 9774 icccntr 9776 fzaddel 9832 fzsubel 9833 mulexp 10325 upxp 12430 uptx 12432 |
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