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Mirrors > Home > MPE Home > Th. List > ad7antr | Structured version Visualization version GIF version |
Description: Deduction adding 7 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 |
---|---|
ad7antr | ⊢ ((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | adantr 483 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓) |
3 | 2 | ad6antr 734 | 1 ⊢ ((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 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: ad8antr 738 ad8antlr 739 simp-7l 787 catpropd 16979 natpropd 17246 ucncn 22894 tgcgrxfr 26304 tgbtwnconn1lem3 26360 tgbtwnconn1 26361 midexlem 26478 lnopp2hpgb 26549 trgcopy 26590 qsidomlem2 30966 lbsdiflsp0 31022 fedgmul 31027 sigapildsys 31421 afsval 31942 matunitlindflem1 34903 dffltz 39291 |
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