Theorem nfsb2 2360

Description: Bound-variable hypothesis builder for substitution. (Contributed by Mario Carneiro, 4-Oct-2016.)

Assertion

Ref	Expression
nfsb2	|- ( -. A. x x = y -> F/ x [ y / x ] ph )

Proof of Theorem nfsb2

Step	Hyp	Ref	Expression
1		nfna1 2029	. 2 |- F/ x -. A. x x = y
2		hbsb2 2359	. 2 |- ( -. A. x x = y -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )
3	1, 2	nf5d 2118	1 |- ( -. A. x x = y -> F/ x [ y / x ] ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   F/wnf 1708   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by:  nfsb4t  2389  sbco3  2417  sb9  2426  wl-nfs1t  33324