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Mirrors > Home > ILE Home > Th. List > simpll2 | GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simpll2 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl2 948 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓) | |
2 | 1 | adantr 271 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∧ w3a 925 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 |
This theorem depends on definitions: df-bi 116 df-3an 927 |
This theorem is referenced by: fidceq 6639 fidifsnen 6640 en2eqpr 6677 iunfidisj 6709 cauappcvgprlemlol 7267 caucvgprlemlol 7290 caucvgprprlemlol 7318 elfzonelfzo 9702 qbtwnre 9729 hashun 10274 subcn2 10761 divalglemex 11261 divalglemeuneg 11262 dvdslegcd 11295 lcmledvds 11391 |
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