Theorem nfcjust 2478

Description: Justification theorem for df-nfc 2479. (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 1619	. . 3 |- F/x y = z
2		eleq1 2413	. . 3 |- (y = z -> (y e. A <-> z e. A))
3	1, 2	nfbidf 1774	. 2 |- (y = z -> ( F/x y e. A <-> F/x z e. A))
4	3	cbvalv 2002	1 |- (A.y F/x y e. A <-> A.z F/x z e. A)

Syntax hints:   <-> wb 176  A.wal 1540   F/wnf 1544   = wceq 1642   e. wcel 1710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-cleq 2346  df-clel 2349

This theorem is referenced by: (None)