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Theorem nfor 1554
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 1500 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfor.2 . . . 4 𝑥𝜓
43nfri 1500 . . 3 (𝜓 → ∀𝑥𝜓)
52, 4hbor 1526 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfi 1439 1 𝑥(𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wo 698  wnf 1437
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-gen 1426  ax-4 1488
This theorem depends on definitions:  df-bi 116  df-nf 1438
This theorem is referenced by:  nfdc  1638  nfun  3236  nfpr  3580  nfso  4231  nffrec  6300  indpi  7173  nfsum1  11156  nfsum  11157  nfcprod1  11354  nfcprod  11355  bj-findis  13346  isomninnlem  13398  trirec0  13410
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