Theorem ad5ant23 758

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 712	. 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	2	ad2antrr 724	1 ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 398

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 209  df-an 399

This theorem is referenced by:  funcpropd  17164  natpropd  17240  pmtr3ncom  18597  dmatscmcl  21106  opreu2reuALT  30234  matunitlindflem2  34883  rexabslelem  41685  hoidmvle  42876