Theorem wl-rgen2w 34880

Description: Generalization rule for restricted quantification. Note that 𝑥 and 𝑦 needn't be distinct. (Contributed by Wolf Lammen, 10-Jun-2023.)

Hypothesis

Ref	Expression
wl-rgenw.1	⊢ 𝜑

Assertion

Ref	Expression
wl-rgen2w	⊢ ∀(𝑥 : 𝐴)∀(𝑦 : 𝐵)𝜑

Proof of Theorem wl-rgen2w

Step	Hyp	Ref	Expression
1		wl-rgenw.1	. . 3 ⊢ 𝜑
2	1	wl-rgenw 34879	. 2 ⊢ ∀(𝑦 : 𝐵)𝜑
3	2	wl-rgenw 34879	1 ⊢ ∀(𝑥 : 𝐴)∀(𝑦 : 𝐵)𝜑

Syntax hints:  ∀wl-ral 34867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1780  df-sb 2069  df-wl-ral 34872

This theorem is referenced by: (None)