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Theorem pm4.71rd 616
 Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by NM, 10-Feb-2005.)
Hypothesis
Ref Expression
pm4.71rd.1 (φ → (ψχ))
Assertion
Ref Expression
pm4.71rd (φ → (ψ ↔ (χ ψ)))

Proof of Theorem pm4.71rd
StepHypRef Expression
1 pm4.71rd.1 . 2 (φ → (ψχ))
2 pm4.71r 612 . 2 ((ψχ) ↔ (ψ ↔ (χ ψ)))
31, 2sylib 188 1 (φ → (ψ ↔ (χ ψ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by:  2reu5  3044  ralss  3332  rexss  3333  nnsucelrlem2  4425  dfco2a  5081  feu  5242  funbrfv2b  5362  dffn5  5363  fnrnfv  5364  fniniseg  5371  eqfnfv2  5393  dff4  5421  dff13  5471  nmembers1lem3  6270
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