Theorem ad9antr 755

Description: Deduction adding 9 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
ad9antr	⊢ ((((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜓)

Proof of Theorem ad9antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	adantr 486	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓)
3	2	ad8antr 753	1 ⊢ ((((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  ad10antr  757  ad10antlr  758  simp-9l  805  isprmidlc  21634  ssdifidlprm  21648  midexlem  29170  footexALT  29199  footex  29202  tgaaddcpbllem1  29355  angmgmaddcpbl  29396  angmgmaddcl  29397  angmgmaddlid  29398  prlngmolem1  29436  f1otrg  29454  2ndresdju  33291  rhmimaidl  34029  qsdrngi  34066  lbsdiflsp0  34305  dimkerim  34306  constrconj  34424  constrfin  34425