Theorem nf3andOLD 2233

Description: Obsolete proof of nf3and 1827 as of 6-Oct-2021. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfandOLD.1	|- ( ph -> F/ x ps )
nfandOLD.2	|- ( ph -> F/ x ch )
nfand.3OLD	|- ( ph -> F/ x th )

Assertion

Ref	Expression
nf3andOLD	|- ( ph -> F/ x ( ps /\ ch /\ th ) )

Proof of Theorem nf3andOLD

Step	Hyp	Ref	Expression
1		df-3an 1039	. 2 |- ( ( ps /\ ch /\ th ) <-> ( ( ps /\ ch ) /\ th ) )
2		nfandOLD.1	. . . 4 |- ( ph -> F/ x ps )
3		nfandOLD.2	. . . 4 |- ( ph -> F/ x ch )
4	2, 3	nfandOLD 2232	. . 3 |- ( ph -> F/ x ( ps /\ ch ) )
5		nfand.3OLD	. . 3 |- ( ph -> F/ x th )
6	4, 5	nfandOLD 2232	. 2 |- ( ph -> F/ x ( ( ps /\ ch ) /\ th ) )
7	1, 6	nfxfrdOLD 1838	1 |- ( ph -> F/ x ( ps /\ ch /\ th ) )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037   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-3an 1039  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by: (None)