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Theorem prth 326
 Description: Theorem *3.47 of [WhiteheadRussell] p. 113. It was proved by Leibniz, and it evidently pleased him enough to call it 'praeclarum theorema' (splendid theorem). (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Assertion
Ref Expression
prth (((φψ) (χθ)) → ((φ χ) → (ψ θ)))

Proof of Theorem prth
StepHypRef Expression
1 simpl 102 . 2 (((φψ) (χθ)) → (φψ))
2 simpr 103 . 2 (((φψ) (χθ)) → (χθ))
31, 2anim12d 318 1 (((φψ) (χθ)) → ((φ χ) → (ψ θ)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97 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:  nfand  1457  equsexd  1614  mo23  1938  euind  2722  reuind  2738  reuss2  3211  opelopabt  3990  reusv3i  4157
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