Theorem ala1 1741

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 1739	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1722  ax-4 1737

This theorem is referenced by:  19.38  1766  nfimdOLDOLD  1824  ax12dgen  2011  ax12  2304  stdpc4  2353  alral  2928  hbimtg  31712  bj-axdd2  32576  bj-alsb  32625  bj-ax12v3ALT  32676  bj-equsal1t  32809