Theorem nfbiOLD 1835

Description: If x is not free in ph and ps, it is not free in (ph <-> ps). (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nf.1	|- F/xph
nf.2	|- F/xps

Assertion

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

Proof of Theorem nfbiOLD

Step	Hyp	Ref	Expression
1		dfbi2 609	. 2 |- ((ph <-> ps) <-> ((ph -> ps) /\ (ps -> ph)))
2		nf.1	. . . 4 |- F/xph
3		nf.2	. . . 4 |- F/xps
4	2, 3	nfim 1813	. . 3 |- F/x(ph -> ps)
5	3, 2	nfim 1813	. . 3 |- F/x(ps -> ph)
6	4, 5	nfan 1824	. 2 |- F/x((ph -> ps) /\ (ps -> ph))
7	1, 6	nfxfr 1570	1 |- F/x(ph <-> ps)

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358   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  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)