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Theorem pm4.38 570
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 107 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜑𝜒))
2 simpr 108 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜓𝜃))
31, 2anbi12d 457 1 (((𝜑𝜒) ∧ (𝜓𝜃)) → ((𝜑𝜓) ↔ (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  xpf1o  6514  isprm3  11025
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