Theorem ad5ant13 755

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Hypothesis

Ref	Expression
ad5ant2.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
ad5ant13	⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant13

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	adantlr 713	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒)
3	2	ad2antrr 724	1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

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:  natpropd  17245  ghmcmn  18951  ustuqtop2  22850  tocyccntz  30786  matunitlindflem1  34887  supxrgelem  41603  xrralrecnnle  41651  limsupvaluz2  42017  supcnvlimsup  42019  meaiuninc3v  42765  smfaddlem1  43038  smflimlem4  43049