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  8625  ixxin  13272  odf1  19484  m2cpmfo  22681  cnflf  23927  cnfcf  23967  tmdmulg  24017  blin  24346  blsscls2  24429  metcn  24468  xrsxmet  24735  sqf11  27086  dimval  33624  dfgcd3  37379  lindsadd  37663  hspmbllem2  46739