Theorem ala1 1811

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 1809	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1793  ax-4 1807

This theorem is referenced by:  19.38  1837  stdpc4  2068  ax12dgen  2134  ax12  2431  sb4a  2488  alral  3081  hbimtg  35770  bj-axdd2  36558  bj-ax12v3ALT  36652  bj-equsal1t  36788