Theorem ala1 1909

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 1907	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1651

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1891  ax-4 1905

This theorem is referenced by:  19.38  1934  ax12dgen  2178  ax12  2430  stdpc4  2469  alral  3109  hbimtg  32224  bj-axdd2  33081  bj-alsb  33132  bj-ax12v3ALT  33182  bj-equsal1t  33304