Theorem nfbii 1569

Description: Equality theorem for not-free. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfbii.1	|- (ph <-> ps)

Assertion

Ref	Expression
nfbii	|- ( F/xph <-> F/xps)

Proof of Theorem nfbii

Step	Hyp	Ref	Expression
1		nfbii.1	. . . 4 |- (ph <-> ps)
2	1	albii 1566	. . . 4 |- (A.xph <-> A.xps)
3	1, 2	imbi12i 316	. . 3 |- ((ph -> A.xph) <-> (ps -> A.xps))
4	3	albii 1566	. 2 |- (A.x(ph -> A.xph) <-> A.x(ps -> A.xps))
5		df-nf 1545	. 2 |- ( F/xph <-> A.x(ph -> A.xph))
6		df-nf 1545	. 2 |- ( F/xps <-> A.x(ps -> A.xps))
7	4, 5, 6	3bitr4i 268	1 |- ( F/xph <-> F/xps)

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-nf 1545

This theorem is referenced by:  nfxfr  1570  nfxfrd  1571  nfceqi  2486  dfnfc2  3910