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Theorem nfnfcALT 2601
Description: Alternate proof of nfnfc 2600. Shorter but requiring more axioms. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
nfnfc.1  |-  F/_ x A
Assertion
Ref Expression
nfnfcALT  |-  F/ x F/_ y A

Proof of Theorem nfnfcALT
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2579 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2584 . . . 4  |-  F/ x  z  e.  A
43nfnf 2007 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 2005 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1692 1  |-  F/ x F/_ y A
Colors of variables: wff setvar class
Syntax hints:   A.wal 1435   F/wnf 1663    e. wcel 1870   F/_wnfc 2577
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ex 1660  df-nf 1664  df-sb 1790  df-cleq 2421  df-clel 2424  df-nfc 2579
This theorem is referenced by: (None)
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