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Theorem wl-nfalv 36901
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 1905 . . 3 (𝜑 → ∀𝑥𝜑)
21hbal 2159 . 2 (∀𝑦𝜑 → ∀𝑥𝑦𝜑)
32nf5i 2134 1 𝑥𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1531  wnf 1777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-10 2129  ax-11 2146
This theorem depends on definitions:  df-bi 206  df-ex 1774  df-nf 1778
This theorem is referenced by: (None)
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