Theorem nfcjust 2296

Description: Justification theorem for df-nfc 2297. (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 1516	. . 3 |- F/ x y = z
2		eleq1 2229	. . 3 |- ( y = z -> ( y e. A <-> z e. A ) )
3	1, 2	nfbidf 1527	. 2 |- ( y = z -> ( F/ x y e. A <-> F/ x z e. A ) )
4	3	cbvalv 1905	1 |- ( A. y F/ x y e. A <-> A. z F/ x z e. A )

Syntax hints:   <-> wb 104   A.wal 1341   F/wnf 1448   e. wcel 2136

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-cleq 2158  df-clel 2161

This theorem is referenced by: (None)