Theorem nfcjust 2338

Description: Justification theorem for df-nfc 2339. (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 1552	. . 3 |- F/ x y = z
2		eleq1 2270	. . 3 |- ( y = z -> ( y e. A <-> z e. A ) )
3	1, 2	nfbidf 1563	. 2 |- ( y = z -> ( F/ x y e. A <-> F/ x z e. A ) )
4	3	cbvalv 1942	1 |- ( A. y F/ x y e. A <-> A. z F/ x z e. A )

Syntax hints:   <-> wb 105   A.wal 1371   F/wnf 1484   e. wcel 2178

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-cleq 2200  df-clel 2203

This theorem is referenced by: (None)