Theorem adantl4r 755

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

Hypothesis

Ref	Expression
adantl4r.1	⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Assertion

Ref	Expression
adantl4r	⊢ ((((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Proof of Theorem adantl4r

Step	Hyp	Ref	Expression
1		adantl4r.1	. . . 4 ⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
2	1	ex 412	. . 3 ⊢ ((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅))
3	2	adantl3r 750	. 2 ⊢ (((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅))
4	3	imp 406	1 ⊢ ((((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

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 207  df-an 396

This theorem is referenced by:  adantl5r  762  perpneq  28723  rhmimaidl  33461  zarclsun  33870  pstmxmet  33897  limsupmnflem  45740  xlimmnfvlem2  45853  xlimpnfvlem2  45857  icccncfext  45907  hspmbllem2  46647