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Mirrors > Home > MPE Home > Th. List > ad5ant14 | 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 |
---|---|
ad5ant14 | ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad5ant2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | adantlr 713 | . 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒) |
3 | 2 | ad4ant13 749 | 1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
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 397 |
This theorem is referenced by: leexp1a 14077 cpmatinvcl 22062 restcld 22519 ustuqtop3 23591 legval 27424 lssdimle 32196 zarcls1 32341 lindsenlbs 36062 matunitlindflem1 36063 xrralrecnnle 43591 limclner 43862 limsupub2 44023 xlimliminflimsup 44073 pimdecfgtioo 44928 pimincfltioo 44929 |
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