Theorem ala1 1840

Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018.)

Assertion

Ref	Expression
ala1	⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Proof of Theorem ala1

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜑 → (𝜓 → 𝜑))
2	1	alimi 1838	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1822  ax-4 1836

This theorem is referenced by:  19.38  1866  stdpc4lem  2104  stdpc4ALT  2106  ax12dgen  2175  ax12  2461  sb4a  2518  alral  3100  hbimtg  36191  mh-regprimbi  36941  bj-axdd2  37070  bj-ala1i  37096  bj-ax12v3ALT  37196  bj-equsal1t  37342