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Theorem nfnfcALT 2629
 Description: Alternative, shorter proof of nfnfc 2628, based on more axioms. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
nfnfc.1
Assertion
Ref Expression
nfnfcALT

Proof of Theorem nfnfcALT
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2607 . 2
2 nfnfc.1 . . . . 5
32nfcri 2612 . . . 4
43nfnf 1949 . . 3
54nfal 1947 . 2
61, 5nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  A.wal 1393  F/wnf 1616  e.wcel 1818  F/_wnfc 2605 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607
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