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Mirrors > Home > MPE Home > Th. List > simp-9r | Structured version Visualization version GIF version |
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
simp-9r | ⊢ ((((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp-8r 815 | . 2 ⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓) | |
2 | 1 | adantr 481 | 1 ⊢ ((((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 |
This theorem is referenced by: simp-10r 819 legso 25494 miriso 25565 footex 25613 f1otrg 25751 |
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