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Mirrors > Home > ILE Home > Th. List > simplr2 | GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simplr2 | ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr2 989 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓) | |
2 | 1 | adantr 274 | 1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∧ w3a 963 |
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 df-3an 965 |
This theorem is referenced by: prarloclemlt 7325 prarloclemlo 7326 seq3f1oleml 10307 resqrexlemdecn 10816 ennnfoneleminc 11960 restopnb 12389 cnptopresti 12446 blsscls2 12701 |
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