Theorem nfbidOLD 2242

Description: Obsolete proof of nfbid 1832 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 29-Dec-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfbidOLD.1	|- ( ph -> F/ x ps )
nfbidOLD.2	|- ( ph -> F/ x ch )

Assertion

Ref	Expression
nfbidOLD	|- ( ph -> F/ x ( ps <-> ch ) )

Proof of Theorem nfbidOLD

Step	Hyp	Ref	Expression
1		dfbi2 660	. 2 |- ( ( ps <-> ch ) <-> ( ( ps -> ch ) /\ ( ch -> ps ) ) )
2		nfbidOLD.1	. . . 4 |- ( ph -> F/ x ps )
3		nfbidOLD.2	. . . 4 |- ( ph -> F/ x ch )
4	2, 3	nfimdOLD 2226	. . 3 |- ( ph -> F/ x ( ps -> ch ) )
5	3, 2	nfimdOLD 2226	. . 3 |- ( ph -> F/ x ( ch -> ps ) )
6	4, 5	nfandOLD 2232	. 2 |- ( ph -> F/ x ( ( ps -> ch ) /\ ( ch -> ps ) ) )
7	1, 6	nfxfrdOLD 1838	1 |- ( ph -> F/ x ( ps <-> ch ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   F/wnfOLD 1709

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

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by:  nfbiOLD  2243