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Theorem nfor 1509
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 1455 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfor.2 . . . 4 𝑥𝜓
43nfri 1455 . . 3 (𝜓 → ∀𝑥𝜓)
52, 4hbor 1481 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfi 1394 1 𝑥(𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wo 662  wnf 1392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-gen 1381  ax-4 1443
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  nfdc  1592  nfun  3145  nfpr  3475  nfso  4103  nffrec  6115  indpi  6845  nfsum1  10635  nfsum  10636  bj-findis  11312
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