Theorem ad4ant124 1174

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 1118	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	adantlr 715	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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  df-3an 1088

This theorem is referenced by:  ad5ant124  1367  naddsuc2  8611  ixxin  13257  odf1  19469  m2cpmfo  22666  cnflf  23912  cnfcf  23952  tmdmulg  24002  blin  24331  blsscls2  24414  metcn  24453  xrsxmet  24720  sqf11  27071  dimval  33605  dfgcd3  37358  lindsadd  37653  hspmbllem2  46665