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Mirrors > Home > ILE Home > Th. List > simp12 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp12 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 950 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓) | |
2 | 1 | 3ad2ant1 970 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 930 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 932 |
This theorem is referenced by: simpl12 1025 simpr12 1034 simp112 1079 simp212 1088 simp312 1097 frecsuclem 6233 dvdsgcd 11493 |
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