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Theorem hbal 2021
Description: If 𝑥 is not free in 𝜑, it is not free in 𝑦𝜑. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
hbal.1 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
hbal (∀𝑦𝜑 → ∀𝑥𝑦𝜑)

Proof of Theorem hbal
StepHypRef Expression
1 hbal.1 . . 3 (𝜑 → ∀𝑥𝜑)
21alimi 1728 . 2 (∀𝑦𝜑 → ∀𝑦𝑥𝜑)
3 ax-11 2019 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
42, 3syl 17 1 (∀𝑦𝜑 → ∀𝑥𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1711  ax-4 1726  ax-11 2019
This theorem is referenced by:  hbex  2135  nfal  2136  cbv3hvOLD  2155  hbral  2922  wl-nfalv  32290
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