Theorem ad5antlr 725

Description: Deduction adding 5 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.) (Proof shortened by Wolf Lammen, 5-Apr-2022.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
ad5antlr	⊢ ((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜓)

Proof of Theorem ad5antlr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	adantl 475	. 2 ⊢ ((𝜒 ∧ 𝜑) → 𝜓)
3	2	ad4antr 722	1 ⊢ ((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 386

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 199  df-an 387

This theorem is referenced by:  restmetu  22787  foresf1o  29909  fimaproj  30502  locfinreflem  30509  pstmxmet  30542  mblfinlem3  34079  itg2gt0cn  34095  dffltz  38222  pell1234qrmulcl  38389  suplesup  40473  limclner  40801  bgoldbtbnd  42732  isomushgr  42749