Theorem ala1 1832

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 1830	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1557

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1814  ax-4 1828

This theorem is referenced by:  19.38  1858  stdpc4lem  2096  stdpc4ALT  2098  ax12dgen  2167  ax12  2453  sb4a  2510  alral  3090  hbimtg  36115  mh-regprimbi  36866  bj-axdd2  36996  bj-ala1i  37022  bj-ax12v3ALT  37122  bj-equsal1t  37268