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Theorem bicom1 220
Description: Commutative law for the biconditional. (Contributed by Wolf Lammen, 10-Nov-2012.)
Assertion
Ref Expression
bicom1 ((𝜑𝜓) → (𝜓𝜑))

Proof of Theorem bicom1
StepHypRef Expression
1 biimpr 219 . 2 ((𝜑𝜓) → (𝜓𝜑))
2 biimp 214 . 2 ((𝜑𝜓) → (𝜑𝜓))
31, 2impbid 211 1 ((𝜑𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205
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 206
This theorem is referenced by:  bicom  221  bicomi  223  nanass  1505  rexsng  4611  nummin  33049  bicomdALT  40150  frege55aid  41432  frege55lem2a  41434  bisaiaisb  44364  confun4  44393  confun5  44394  ichnfim  44872
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