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Theorem pm4.38 537
Description: Theorem *4.38 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.38 (((φχ) (ψθ)) → ((φ ψ) ↔ (χ θ)))

Proof of Theorem pm4.38
StepHypRef Expression
1 simpl 102 . 2 (((φχ) (ψθ)) → (φχ))
2 simpr 103 . 2 (((φχ) (ψθ)) → (ψθ))
31, 2anbi12d 442 1 (((φχ) (ψθ)) → ((φ ψ) ↔ (χ θ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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