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Theorem compleqi 3244
 Description: Equality inference for complement. (Contributed by SF, 11-Jan-2015.)
Hypothesis
Ref Expression
compleqi.1 A = B
Assertion
Ref Expression
compleqi A = ∼ B

Proof of Theorem compleqi
StepHypRef Expression
1 compleqi.1 . 2 A = B
2 compleq 3243 . 2 (A = B → ∼ A = ∼ B)
31, 2ax-mp 8 1 A = ∼ B
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∼ ccompl 3205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212 This theorem is referenced by:  dfin5  3545  dfun4  3546  iunin  3547  iinun  3548  compl0  4071  incompl  4073  nnadjoin  4520  nnadjoinpw  4521  nulnnn  4556  sbthlem1  6203
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