Theorem ala1 1817

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 1815	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1799  ax-4 1813

This theorem is referenced by:  19.38  1842  stdpc4  2072  ax12dgen  2132  ax12  2423  sb4a  2484  alral  3079  hbimtg  33688  bj-axdd2  34701  bj-ax12v3ALT  34795  bj-equsal1t  34932