Theorem ad4ant124 1192

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

Hypothesis

Ref	Expression
ad4ant3.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
ad4ant124	⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant124

Step	Hyp	Ref	Expression
1		ad4ant3.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3expa 1136	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	adantlr 728	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  ad5ant124OLD  1389  ad5ant135  1394  naddsuc2  8704  ixxin  13486  odf1  19769  m2cpmfo  23067  cnflf  24314  cnfcf  24354  tmdmulg  24404  blin  24733  blsscls2  24816  metcn  24855  xrsxmet  25122  sqf11  27459  dimval  34226  dfgcd3  38225  lindsadd  38516  hspmbllem2  47606