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Theorem bicom 191
Description: Commutative law for equivalence. Theorem *4.21 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
bicom ((φψ) ↔ (ψφ))

Proof of Theorem bicom
StepHypRef Expression
1 bicom1 190 . 2 ((φψ) → (ψφ))
2 bicom1 190 . 2 ((ψφ) → (φψ))
31, 2impbii 180 1 ((φψ) ↔ (ψφ))
Colors of variables: wff setvar class
Syntax hints:  wb 176
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 177
This theorem is referenced by:  bicomd  192  bibi1i  305  bibi1d  310  con2bi  318  ibibr  332  bibif  335  nbbn  347  pm5.17  858  biluk  899  bigolden  901  xorcom  1307  falbitru  1352  3impexpbicom  1367  mtp-xorOLD  1537  exists1  2293  eqcom  2355  abeq1  2459  ssequn1  3433  isocnv  5491
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