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Mirrors > Home > ILE Home > Th. List > 3anidm13 | GIF version |
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.) |
Ref | Expression |
---|---|
3anidm13.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜑) → 𝜒) |
Ref | Expression |
---|---|
3anidm13 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anidm13.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜑) → 𝜒) | |
2 | 1 | 3com23 1110 | . 2 ⊢ ((𝜑 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
3 | 2 | 3anidm12 1192 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∧ w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: ltnsym 7104 npncan2 7238 ltsubpos 7449 leaddle0 7472 subge02 7473 halfaddsub 8159 avglt1 8163 |
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