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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 8615 cofsmo 10307 leexp1a 14212 natpropd 18033 mhpmulcl 22171 isucn2 24304 metust 24587 hpgerlem 28788 clwlkclwwlklem2a4 30026 cyc3genpm 33155 nsgqusf1olem1 33421 1arithufdlem2 33553 ist0cld 33794 matunitlindflem1 37603 rexabslelem 45368 |
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