Theorem xchbinx 683

Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)

Hypotheses

Ref	Expression
xchbinx.1	|- ( ph <-> -. ps )
xchbinx.2	|- ( ps <-> ch )

Assertion

Ref	Expression
xchbinx	|- ( ph <-> -. ch )

Proof of Theorem xchbinx

Step	Hyp	Ref	Expression
1		xchbinx.1	. 2 |- ( ph <-> -. ps )
2		xchbinx.2	. . 3 |- ( ps <-> ch )
3	2	notbii 669	. 2 |- ( -. ps <-> -. ch )
4	1, 3	bitri 184	1 |- ( ph <-> -. ch )

Syntax hints:   -. wn 3   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  xchbinxr  684  necon3abii  2403  elirr  4577  en2lp  4590  dm0rn0  4883