Theorem ad4ant123 1171

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
ad4ant123	⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜃)

Proof of Theorem ad4ant123

Step	Hyp	Ref	Expression
1		ad4ant3.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3expa 1117	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	adantr 481	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  fin1a2lem11  10166  wrdl3s3  14677  usgr2pthlem  28131  grplsmid  31592  satfrel  33329  uzindd  39985  4animp1  42117  hspmbllem2  44165