Theorem ad7antr 734

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 479	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓)
3	2	ad6antr 732	1 ⊢ ((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394

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 206  df-an 395

This theorem is referenced by:  ad8antr  736  ad8antlr  737  simp-7l  785  catpropd  17657  natpropd  17933  ucncn  24010  tgcgrxfr  28036  tgbtwnconn1lem3  28092  tgbtwnconn1  28093  midexlem  28210  lnopp2hpgb  28281  trgcopy  28322  mgcf1o  32440  elrspunidl  32820  rhmimaidl  32824  qsidomlem2  32846  mxidlirredi  32861  lbsdiflsp0  32999  fedgmul  33004  zarcmplem  33159  sigapildsys  33458  afsval  33981  matunitlindflem1  36787  dffltz  41678