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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 712 | . 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒) |
3 | 2 | ad4ant13 749 | 1 ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 |
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 209 df-an 399 |
This theorem is referenced by: omlimcl 8198 cofsmo 9685 leexp1a 13533 natpropd 17240 isucn2 22882 metust 23162 hpgerlem 26545 clwlkclwwlklem2a4 27769 cyc3genpm 30789 matunitlindflem1 34882 rexabslelem 41685 |
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