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Mirrors > Home > MPE Home > Th. List > ad6antlr | Structured version Visualization version GIF version |
Description: Deduction adding 6 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.) (Proof shortened by Wolf Lammen, 5-Apr-2022.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad6antlr | ⊢ (((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | adantl 483 | . 2 ⊢ ((𝜒 ∧ 𝜑) → 𝜓) |
3 | 2 | ad5antr 733 | 1 ⊢ (((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 |
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 206 df-an 398 |
This theorem is referenced by: simp-6r 787 elrspunidl 32206 lbsdiflsp0 32324 locfinreflem 32424 heicant 36116 itg2gt0cn 36136 ftc1anclem7 36160 dffltz 40975 omabs2 41668 cfsetsnfsetfo 45301 isomuspgrlem1 46026 |
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