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Theorem ala1 1805
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 1803 1 (∀𝑥𝜑 → ∀𝑥(𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1787  ax-4 1801
This theorem is referenced by:  19.38  1830  stdpc4  2064  ax12dgen  2129  ax12  2437  sb4a  2502  stdpc4ALT  2583  alral  3151  hbimtg  32948  bj-axdd2  33823  bj-ax12v3ALT  33917  bj-equsal1t  34042
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