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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 472 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
3 | 2 | ad7antr 783 | 1 ⊢ (((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 197 df-an 385 |
This theorem is referenced by: ad9antr 791 ad9antrOLD 792 ad9antlr 793 simp-8l 841 simp-9r 847 legso 25714 miriso 25785 midexlem 25807 opphl 25866 trgcopy 25916 inaghl 25951 qtophaus 30233 afsval 31079 hoidmvle 41338 smfmullem3 41524 |
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