Theorem nfcjust 2207

Description: Justification theorem for df-nfc 2208. (Contributed by Mario Carneiro, 13-Oct-2016.)

Assertion

Ref	Expression
nfcjust	|- ( A. y F/ x y e. A <-> A. z F/ x z e. A )

Distinct variable groups:   x, y, z   y, A, z

Allowed substitution hint:   A( x)

Proof of Theorem nfcjust

Step	Hyp	Ref	Expression
1		nfv 1461	. . 3 |- F/ x y = z
2		eleq1 2141	. . 3 |- ( y = z -> ( y e. A <-> z e. A ) )
3	1, 2	nfbidf 1472	. 2 |- ( y = z -> ( F/ x y e. A <-> F/ x z e. A ) )
4	3	cbvalv 1835	1 |- ( A. y F/ x y e. A <-> A. z F/ x z e. A )

Syntax hints:   <-> wb 103   A.wal 1282   F/wnf 1389   e. wcel 1433

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-cleq 2074  df-clel 2077

This theorem is referenced by: (None)