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| Mirrors > Home > MPE Home > Th. List > ad5ant24 | Structured version Visualization version GIF version | ||
| Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.) | 
| Ref | Expression | 
|---|---|
| ad5ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | 
| Ref | Expression | 
|---|---|
| ad5ant24 | ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ad5ant2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 2 | 1 | adantll 714 | . 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒) | 
| 3 | 2 | ad4ant13 751 | 1 ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 | 
| 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 207 df-an 396 | 
| This theorem is referenced by: omlimcl 8617 cofsmo 10310 leexp1a 14216 natpropd 18025 mhpmulcl 22154 isucn2 24289 metust 24572 hpgerlem 28774 clwlkclwwlklem2a4 30017 cyc3genpm 33173 nsgqusf1olem1 33442 1arithufdlem2 33574 ist0cld 33833 matunitlindflem1 37624 rexabslelem 45434 | 
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