Theorem nfcjust 2307

Description: Justification theorem for df-nfc 2308. (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 1528	. . 3 |- F/ x y = z
2		eleq1 2240	. . 3 |- ( y = z -> ( y e. A <-> z e. A ) )
3	1, 2	nfbidf 1539	. 2 |- ( y = z -> ( F/ x y e. A <-> F/ x z e. A ) )
4	3	cbvalv 1917	1 |- ( A. y F/ x y e. A <-> A. z F/ x z e. A )

Syntax hints:   <-> wb 105   A.wal 1351   F/wnf 1460   e. wcel 2148

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-cleq 2170  df-clel 2173

This theorem is referenced by: (None)