Theorem ad10antr 754

Description: Deduction adding 10 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
ad10antr	⊢ (((((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) ∧ 𝜅) → 𝜓)

Proof of Theorem ad10antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	adantr 484	. 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜓)
3	2	ad9antr 752	1 ⊢ (((((((((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) ∧ 𝜅) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399

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 209  df-an 400

This theorem is referenced by:  simp-10l  804  simp-11l  806  simp-11r  807  footexALT  28891  footex  28894  lnopp2hpgb  28936  ad11antr  32650  rloccring  33452  qsdrngi  33683  1arithidom  33733  constrfin  34043