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Mirrors > Home > MPE Home > Th. List > ad5ant134 | 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 |
---|---|
ad5ant134 | ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad5ant.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | ad4ant134 1175 | . 2 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃) |
3 | 2 | adantr 484 | 1 ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1088 |
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 210 df-an 400 df-3an 1090 |
This theorem is referenced by: qsidomlem1 31192 suplesup 42400 limsupvaluz2 42805 supcnvlimsup 42807 limsupgtlem 42844 xlimmnfvlem2 42900 xlimmnfv 42901 xlimpnfvlem2 42904 xlimpnfv 42905 sge0cl 43445 hspmbllem2 43691 |
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