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Theorem pm4.38 579
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 108 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜑𝜒))
2 simpr 109 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → (𝜓𝜃))
31, 2anbi12d 464 1 (((𝜑𝜒) ∧ (𝜓𝜃)) → ((𝜑𝜓) ↔ (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  xpf1o  6706  isprm3  11726
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