Theorem xchbinx 334

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

Hypotheses

Ref	Expression
xchbinx.1	⊢ (𝜑 ↔ ¬ 𝜓)
xchbinx.2	⊢ (𝜓 ↔ 𝜒)

Assertion

Ref	Expression
xchbinx	⊢ (𝜑 ↔ ¬ 𝜒)

Proof of Theorem xchbinx

Step	Hyp	Ref	Expression
1		xchbinx.1	. 2 ⊢ (𝜑 ↔ ¬ 𝜓)
2		xchbinx.2	. . 3 ⊢ (𝜓 ↔ 𝜒)
3	2	notbii 320	. 2 ⊢ (¬ 𝜓 ↔ ¬ 𝜒)
4	1, 3	bitri 275	1 ⊢ (𝜑 ↔ ¬ 𝜒)

Syntax hints:  ¬ wn 3   ↔ wb 206

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207

This theorem is referenced by:  xchbinxr  335  con1bii  356  anor  984  pm4.52  986  pm4.54  988  xordi  1018  xorcom  1514  xorneg1  1522  xorbi12i  1524  norcom  1530  nornot  1531  noran  1532  trunanfal  1582  truxortru  1585  truxorfal  1586  falxorfal  1588  trunortru  1589  trunorfal  1590  falnorfal  1592  nic-mpALT  1672  nic-axALT  1674  sbex  2281  necon3abii  2971  ne3anior  3019  rexab  3657  inssdif0  4327  falseral0  4469  dtruALT  5330  dm0rn0  5871  brprcneu  6816  brprcneuALT  6817  soseq  8099  0nelfz1  13464  pmltpc  25367  cofcutr  27855  nbgrnself  29322  rgrx0ndm  29557  clwwlkneq0  29991  nfrgr2v  30234  frgrncvvdeqlem1  30261  cvbr2  32245  bnj1143  34759  fmlan0  35366  brsset  35865  brtxpsd  35870  dffun10  35890  dfint3  35928  brub  35930  wl-nfeqfb  37512  sbcni  38093  brvdif2  38239  dfssr2  38478  lcvbr2  39003  atlrelat1  39302  dfxor5  43743  df3an2  43745  clsk1independent  44022  spr0nelg  47464  341fppr2  47722  9fppr8  47725  pgrpgt2nabl  48354  lmod1zrnlvec  48483  aacllem  49790