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Mirrors > Home > ILE Home > Th. List > anabsi7 | GIF version |
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.) |
Ref | Expression |
---|---|
anabsi7.1 | ⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜒)) |
Ref | Expression |
---|---|
anabsi7 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabsi7.1 | . . 3 ⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜒)) | |
2 | 1 | anabsi6 580 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
3 | 2 | ancoms 268 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: syl2an23an 1299 nelrdva 2944 elunii 3812 ordelord 4378 onsucuni2 4560 funfveu 5524 fvelrn 5643 phplem3g 6850 prdisj 7479 gcdmultiplez 12002 dvdssq 12012 |
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