Theorem ad5antlr 733

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 484	. 2 ⊢ ((𝜒 ∧ 𝜑) → 𝜓)
3	2	ad4antr 730	1 ⊢ ((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 398

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 399

This theorem is referenced by:  simp-5r  784  fimaproj  7815  restmetu  23163  foresf1o  30250  nn0xmulclb  30482  fedgmul  31037  locfinreflem  31114  pstmxmet  31147  satfdmlem  32622  mblfinlem3  34965  itg2gt0cn  34981  dffltz  39363  pell1234qrmulcl  39544  suplesup  41697  limclner  42022  bgoldbtbnd  44059  isomushgr  44076