Theorem ala1 1814

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 1812	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1796  ax-4 1810

This theorem is referenced by:  19.38  1839  stdpc4  2073  ax12dgen  2138  ax12  2445  sb4a  2509  stdpc4ALT  2590  alral  3154  hbimtg  33051  bj-axdd2  33926  bj-ax12v3ALT  34020  bj-equsal1t  34145