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Mirrors > Home > MPE Home > Th. List > ad5ant135 | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) |
Ref | Expression |
---|---|
ad5ant.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
ad5ant135 | ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad5ant.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | ad4ant134 1170 | . 2 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃) |
3 | 2 | adantlr 713 | 1 ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 ∧ w3a 1083 |
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 df-3an 1085 |
This theorem is referenced by: supxrgelem 41598 rexabslelem 41685 meaiuninc3v 42760 hoicvr 42824 hspmbllem2 42903 smfaddlem1 43033 |
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