Theorem ad7antr 738

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	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
ad7antr	⊢ ((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Proof of Theorem ad7antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	adantr 480	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓)
3	2	ad6antr 736	1 ⊢ ((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 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:  ad8antr  740  ad8antlr  741  simp-7l  789  catpropd  17753  natpropd  18032  ucncn  24309  tgcgrxfr  28540  tgbtwnconn1lem3  28596  tgbtwnconn1  28597  midexlem  28714  lnopp2hpgb  28785  trgcopy  28826  mgcf1o  32977  chnub  32985  elrgspnlem4  33234  elrspunidl  33435  rhmimaidl  33439  qsidomlem2  33460  ssdifidlprm  33465  mxidlirredi  33478  1arithufdlem3  33553  lbsdiflsp0  33653  fedgmul  33658  constrconj  33749  constrelextdg2  33751  zarcmplem  33841  sigapildsys  34142  afsval  34664  matunitlindflem1  37602  aks6d1c2lem4  42108  dffltz  42620