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Theorem anim12 341
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
anim12  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  /\  ch )  ->  ( ps  /\  th ) ) )

Proof of Theorem anim12
StepHypRef Expression
1 simpl 108 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  ( ph  ->  ps ) )
2 simpr 109 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  ( ch  ->  th ) )
31, 2anim12d 333 1  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  /\  ch )  ->  ( ps  /\  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
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:  nfand  1547  equsexd  1707  mo23  2040  euind  2871  reuind  2889  reuss2  3356  opelopabt  4184  reusv3i  4380  rexanre  11004  bj-stan  13039
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