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Theorem nfor 1903
Description: If 𝑥 is not free in 𝜑 and 𝜓, then it is not free in (𝜑𝜓). (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nf.1 𝑥𝜑
nf.2 𝑥𝜓
Assertion
Ref Expression
nfor 𝑥(𝜑𝜓)

Proof of Theorem nfor
StepHypRef Expression
1 df-or 847 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
2 nf.1 . . . 4 𝑥𝜑
32nfn 1856 . . 3 𝑥 ¬ 𝜑
4 nf.2 . . 3 𝑥𝜓
53, 4nfim 1895 . 2 𝑥𝜑𝜓)
61, 5nfxfr 1851 1 𝑥(𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 846  wnf 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-ex 1778  df-nf 1782
This theorem is referenced by:  nf3or  1904  axi12  2709  axbnd  2710  nfun  4193  nfunOLD  4194  nfpr  4715  rabsnifsb  4747  disjxun  5164  fsuppmapnn0fiubex  14043  nfsum1  15738  nfsum  15739  nfcprod1  15956  nfcprod  15957  fdc1  37706  dvdsrabdioph  42766  mnringmulrcld  44197  disjinfi  45099  iundjiun  46381
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