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.

Step	Hyp	Ref	Expression
1		df-nfc 2607	. 2
2		nfnfc.1	. . . . 5
3	2	nfcri 2612	. . . 4
4	3	nfnf 1949	. . 3
5	4	nfal 1947	. 2
6	1, 5	nfxfr 1645	1

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