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Theorem notbii 593
Description: Negate both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
notbii.1 (φψ)
Assertion
Ref Expression
notbii φ ↔ ¬ ψ)

Proof of Theorem notbii
StepHypRef Expression
1 notbii.1 . 2 (φψ)
2 id 19 . . 3 ((φψ) → (φψ))
32notbid 591 . 2 ((φψ) → (¬ φ ↔ ¬ ψ))
41, 3ax-mp 7 1 φ ↔ ¬ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  sylnbi  602  xchnxbi  604  xchbinx  606  dcbii  746  xorcom  1276  xordidc  1287  sbn  1823  neirr  2210  ssddif  3165  difin  3168  difundi  3183  difindiss  3185  indifdir  3187  rabeq0  3241  abeq0  3242  snprc  3426  difprsnss  3493  uni0b  3596  brdif  3803  unidif0  3911  dtruex  4237  difopab  4412  cnvdif  4673  imadiflem  4921  imadif  4922  brprcneu  5114  poxp  5794  prltlu  6470  recexprlemdisj  6602  axpre-apti  6769  fzdifsuc  8713  fzp1nel  8736  nndc  9235
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