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Mirrors > Home > MPE Home > Th. List > ad8antr | Structured version Visualization version GIF version |
Description: Deduction adding 8 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 5-Apr-2022.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad8antr | ⊢ (((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | adantr 483 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
3 | 2 | ad7antr 736 | 1 ⊢ (((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓) |
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: ad9antr 740 ad9antlr 741 simp-8l 789 legso 26385 miriso 26456 midexlem 26478 opphl 26540 trgcopy 26590 inaghl 26631 cyc3conja 30799 lbsdiflsp0 31022 dimkerim 31023 fedgmul 31027 qtophaus 31100 afsval 31942 dffltz 39291 hoidmvle 42902 smfmullem3 43088 |
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