Theorem ala1 1815

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 1813	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1797  ax-4 1811

This theorem is referenced by:  19.38  1841  stdpc4  2071  ax12dgen  2130  ax12  2422  sb4a  2479  alral  3075  hbimtg  34766  bj-axdd2  35458  bj-ax12v3ALT  35552  bj-equsal1t  35688