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Theorem pm4.45 708
Description: Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.45 (𝜑 ↔ (𝜑 ∧ (𝜑𝜓)))

Proof of Theorem pm4.45
StepHypRef Expression
1 orc 643 . 2 (𝜑 → (𝜑𝜓))
21pm4.71i 377 1 (𝜑 ↔ (𝜑 ∧ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  dn1dc  878
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