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Theorem ad7antr 724
Description: Deduction adding 7 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 5-Apr-2022.)
Hypothesis
Ref Expression
ad2ant.1 (𝜑𝜓)
Assertion
Ref Expression
ad7antr ((((((((𝜑𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Proof of Theorem ad7antr
StepHypRef Expression
1 ad2ant.1 . . 3 (𝜑𝜓)
21adantr 466 . 2 ((𝜑𝜒) → 𝜓)
32ad6antr 720 1 ((((((((𝜑𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 383
This theorem is referenced by:  ad8antr  728  ad8antrOLD  729  ad8antlr  730  simp-7l  780  simp-8r  786  catpropd  16576  natpropd  16843  ucncn  22309  tgcgrxfr  25634  tgbtwnconn1lem3  25690  tgbtwnconn1  25691  midexlem  25808  lnopp2hpgb  25876  trgcopy  25917  sigapildsys  30565  afsval  31089  matunitlindflem1  33738
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