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Theorem hbnt 1521
Description: Closed theorem version of bound-variable hypothesis builder hbn 1522. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
Assertion
Ref Expression
hbnt (x(φxφ) → (¬ φx ¬ φ))

Proof of Theorem hbnt
StepHypRef Expression
1 ax-4 1377 . . . 4 (xφφ)
21con3i 549 . . 3 φ → ¬ xφ)
3 ax6b 1519 . . 3 xφx ¬ xφ)
42, 3syl 14 . 2 φx ¬ xφ)
5 con3 558 . . 3 ((φxφ) → (¬ xφ → ¬ φ))
65al2imi 1323 . 2 (x(φxφ) → (x ¬ xφx ¬ φ))
74, 6syl5 28 1 (x(φxφ) → (¬ φx ¬ φ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1224
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-in1 532  ax-in2 533  ax-5 1312  ax-gen 1314  ax-ie2 1360  ax-4 1377  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-fal 1232
This theorem is referenced by:  hbn  1522  hbnd  1523  nfnt  1524
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