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Theorem wl-nfalv 33628
Description: If 𝑥 is not present in 𝜑, it is not free in 𝑦𝜑. (Contributed by Wolf Lammen, 11-Jan-2020.)
Assertion
Ref Expression
wl-nfalv 𝑥𝑦𝜑
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜑(𝑦)

Proof of Theorem wl-nfalv
StepHypRef Expression
1 ax-5 2001 . . 3 (𝜑 → ∀𝑥𝜑)
21hbal 2204 . 2 (∀𝑦𝜑 → ∀𝑥𝑦𝜑)
32nf5i 2191 1 𝑥𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1635  wnf 1863
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-10 2186  ax-11 2202
This theorem depends on definitions:  df-bi 198  df-ex 1860  df-nf 1864
This theorem is referenced by: (None)
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