Theorem ala1 1755

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 1730	1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1713  ax-4 1728

This theorem is referenced by:  19.38  1757  nfimd  1812  ax12dgen  1998  ax12  2292  stdpc4  2341  alral  2912  hbimtg  30956  bj-axdd2  31749  bj-alsb  31814  bj-ax12v3ALT  31863  bj-equsal1t  31997