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Theorem nfor 1482
Description: If 𝑥 is not free in 𝜑 and 𝜓, it is not free in (𝜑𝜓). (Contributed by Jim Kingdon, 11-Mar-2018.)
Hypotheses
Ref Expression
nfor.1 𝑥𝜑
nfor.2 𝑥𝜓
Assertion
Ref Expression
nfor 𝑥(𝜑𝜓)

Proof of Theorem nfor
StepHypRef Expression
1 nfor.1 . . . 4 𝑥𝜑
21nfri 1428 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfor.2 . . . 4 𝑥𝜓
43nfri 1428 . . 3 (𝜓 → ∀𝑥𝜓)
52, 4hbor 1454 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfi 1367 1 𝑥(𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wo 639  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-gen 1354  ax-4 1416
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nfdc  1565  nfun  3127  nfpr  3448  nfso  4067  nffrec  6013  indpi  6498  nfsum1  10106  nfsum  10107  bj-findis  10491
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