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Mirrors > Home > MPE Home > Th. List > adantl4r | Structured version Visualization version GIF version |
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.) |
Ref | Expression |
---|---|
adantl4r.1 | ⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) |
Ref | Expression |
---|---|
adantl4r | ⊢ ((((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | adantl4r.1 | . . . 4 ⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) | |
2 | 1 | ex 416 | . . 3 ⊢ ((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅)) |
3 | 2 | adantl3r 750 | . 2 ⊢ (((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅)) |
4 | 3 | imp 410 | 1 ⊢ ((((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 |
This theorem is referenced by: adantl5r 763 perpneq 26805 rhmimaidl 31323 zarclsun 31534 pstmxmet 31561 limsupmnflem 42936 xlimmnfvlem2 43049 xlimpnfvlem2 43053 icccncfext 43103 hspmbllem2 43840 |
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