Theorem nfcr 2482

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfcr	|- ( F/_xA -> F/x y e. A)

Distinct variable groups:   x,y   y,A

Allowed substitution hint:   A(x)

Proof of Theorem nfcr

Step	Hyp	Ref	Expression
1		df-nfc 2479	. 2 |- ( F/_xA <-> A.y F/x y e. A)
2		sp 1747	. 2 |- (A.y F/x y e. A -> F/x y e. A)
3	1, 2	sylbi 187	1 |- ( F/_xA -> F/x y e. A)

Syntax hints:   -> wi 4  A.wal 1540   F/wnf 1544   e. wcel 1710   F/_wnfc 2477

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-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nfc 2479

This theorem is referenced by:  nfcrii  2483  nfcrd  2503  abidnf  3006  csbtt  3149  csbnestgf  3185