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Mirrors > Home > ILE Home > Th. List > simp-4l | GIF version |
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
simp-4l | ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simplll 503 | . 2 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑) | |
2 | 1 | adantr 272 | 1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
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 is referenced by: simp-5l 513 disjiun 3870 fnfi 6753 sumeq2 10967 zsumdc 10992 modfsummod 11066 cncnp 12180 |
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