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Theorem pm4.39 910
Description: Theorem *4.39 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.39 (((𝜑𝜒) ∧ (𝜓𝜃)) → ((𝜑𝜓) ↔ (𝜒𝜃)))

Proof of Theorem pm4.39
StepHypRef Expression
1 simpl 471 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜑𝜒))
2 simpr 475 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜓𝜃))
31, 2orbi12d 741 1 (((𝜑𝜒) ∧ (𝜓𝜃)) → ((𝜑𝜓) ↔ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wo 381  wa 382
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 195  df-or 383  df-an 384
This theorem is referenced by:  3orbi123VD  37910
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