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Theorem nfrimi 1415
Description: Moving an antecedent outside . (Contributed by Jim Kingdon, 23-Mar-2018.)
Hypotheses
Ref Expression
nfrimi.1 xφ
nfrimi.2 x(φψ)
Assertion
Ref Expression
nfrimi (φ → Ⅎxψ)

Proof of Theorem nfrimi
StepHypRef Expression
1 nfrimi.1 . 2 xφ
2 nfrimi.2 . . . . 5 x(φψ)
32nfri 1409 . . . 4 ((φψ) → x(φψ))
41nfri 1409 . . . 4 (φxφ)
5 ax-5 1333 . . . 4 (x(φψ) → (xφxψ))
63, 4, 5syl2im 34 . . 3 ((φψ) → (φxψ))
76pm2.86i 92 . 2 (φ → (ψxψ))
81, 7nfd 1413 1 (φ → Ⅎxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  hbsbd  1855
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