Theorem ad5ant15 758

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
ad5ant15	⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)

Proof of Theorem ad5ant15

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	adantlr 715	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒)
3	2	ad4ant14 752	1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  summolem2  15689  ntrivcvg  15870  xkoccn  23513  abelthlem8  26356  rpvmasum2  27430  mulog2sumlem2  27453  f1otrge  28806  nn0xmulclb  32701  intlidl  33398  ply1degltdimlem  33625  fedgmul  33634  cos9thpiminplylem2  33780  signstfvneq0  34570  breprexplemc  34630  mblfinlem2  37659  supxrgelem  45340  supxrge  45341  rexabslelem  45421  uzub  45434  smflimlem4  46779  grimcnv  47892  iinfsubc  49051