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Theorem ala1 1909
Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
ala1 (∀𝑥𝜑 → ∀𝑥(𝜓𝜑))

Proof of Theorem ala1
StepHypRef Expression
1 ax-1 6 . 2 (𝜑 → (𝜓𝜑))
21alimi 1907 1 (∀𝑥𝜑 → ∀𝑥(𝜓𝜑))
Colors of variables: wff setvar class
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
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