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Theorem hbal 1382
Description: If 𝑥 is not free in 𝜑, it is not free in 𝑦𝜑. (Contributed by NM, 5-Aug-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 1360 . 2 (∀𝑦𝜑 → ∀𝑦𝑥𝜑)
3 ax-7 1353 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
42, 3syl 14 1 (∀𝑦𝜑 → ∀𝑥𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1352  ax-7 1353  ax-gen 1354
This theorem is referenced by:  hba2  1459  nfal  1484  aaanh  1494  hbex  1543  pm11.53  1791  euf  1921  hbral  2370
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