Theorem ad9antr 754

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 485	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓)
3	2	ad8antr 752	1 ⊢ ((((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400

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 210  df-an 401

This theorem is referenced by:  ad10antr  756  ad10antlr  757  simp-9l  804  isprmidlc  21439  ssdifidlprm  21451  midexlem  28927  footexALT  28953  footex  28956  prlngmolem1  29151  f1otrg  29157  2ndresdju  32931  rhmimaidl  33680  qsdrngi  33718  lbsdiflsp0  33957  dimkerim  33958  constrconj  34076  constrfin  34077