Theorem adantl4r 765

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 416	. . 3 ⊢ ((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅))
3	2	adantl3r 760	. 2 ⊢ (((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅))
4	3	imp 410	1 ⊢ ((((((𝜑 ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Syntax hints:   → wi 4   ∧ wa 399

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 400

This theorem is referenced by:  adantl5r  772  perpneq  28887  rhmimaidl  33618  zarclsun  34167  pstmxmet  34194  limsupmnflem  46294  xlimmnfvlem2  46407  xlimpnfvlem2  46411  icccncfext  46461  hspmbllem2  47201