Theorem adantl3r 786

Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)

Hypothesis

Ref	Expression
adantl3r.1	⊢ ((((𝜑 ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Assertion

Ref	Expression
adantl3r	⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Proof of Theorem adantl3r

Step	Hyp	Ref	Expression
1		adantl3r.1	. . . 4 ⊢ ((((𝜑 ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
2	1	ex 450	. . 3 ⊢ (((𝜑 ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅))
3	2	adantllr 755	. 2 ⊢ ((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅))
4	3	imp 445	1 ⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Syntax hints:   → wi 4   ∧ wa 384

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 197  df-an 386

This theorem is referenced by:  adantl4r  787  ad5ant1345  1316  iscgrglt  25409  legov  25480  dfcgra2  25721  omssubadd  30362  circlemeth  30718  poimirlem29  33438  adantlllr  39199  climxlim2lem  40071  hspmbllem2  40841