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Theorem nfor 1585
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 1530 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfor.2 . . . 4 𝑥𝜓
43nfri 1530 . . 3 (𝜓 → ∀𝑥𝜓)
52, 4hbor 1557 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfi 1473 1 𝑥(𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wo 709  wnf 1471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-gen 1460  ax-4 1521
This theorem depends on definitions:  df-bi 117  df-nf 1472
This theorem is referenced by:  nfdc  1670  nfun  3306  nfpr  3660  nfso  4323  nffrec  6425  indpi  7376  nfsum1  11405  nfsum  11406  nfcprod1  11603  nfcprod  11604  bj-findis  15217  isomninnlem  15266  trirec0  15280
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