Theorem ad5ant23 756

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
ad5ant23	⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant23

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	adantll 710	. 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	2	ad2antrr 722	1 ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 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 206  df-an 396

This theorem is referenced by:  funcpropd  17532  natpropd  17610  pmtr3ncom  18998  dmatscmcl  21560  opreu2reuALT  30726  matunitlindflem2  35701  rexabslelem  42848  hoidmvle  44028