Theorem xchbinx 672

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 658	. 2 |- ( -. ps <-> -. ch )
4	1, 3	bitri 183	1 |- ( ph <-> -. ch )

Syntax hints:   -. wn 3   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  xchbinxr  673  necon3abii  2372  elirr  4518  en2lp  4531  dm0rn0  4821