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Theorem pm4.38 638
Description: Theorem *4.38 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.38 (((𝜑𝜒) ∧ (𝜓𝜃)) → ((𝜑𝜓) ↔ (𝜒𝜃)))

Proof of Theorem pm4.38
StepHypRef Expression
1 simpl 486 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜑𝜒))
2 simpr 488 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜓𝜃))
31, 2anbi12d 634 1 (((𝜑𝜒) ∧ (𝜓𝜃)) → ((𝜑𝜓) ↔ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  bi2anan9  639  xpf1o  8722  isprm3  16117  csbingVD  42026  csbxpgVD  42036  csbunigVD  42040  ichan  44425
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