Theorem ad8antr 740

Description: Deduction adding 8 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 5-Apr-2022.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
ad8antr	⊢ (((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

Proof of Theorem ad8antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	adantr 480	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓)
3	2	ad7antr 738	1 ⊢ (((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  ad9antr  742  ad9antlr  743  simp-8l  790  legso  28578  miriso  28649  midexlem  28671  opphl  28733  trgcopy  28783  inaghl  28824  cyc3conja  33124  elrgspnlem4  33210  rloccring  33235  ssdifidlprm  33421  mxidlirred  33435  qsdrngi  33458  1arithidom  33500  1arithufdlem3  33509  lbsdiflsp0  33637  dimkerim  33638  fedgmul  33642  constrelextdg2  33758  qtophaus  33847  zarcmplem  33892  afsval  34682  dffltz  42673  hoidmvle  46644  smfmullem3  46837