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Theorem anim12ii 554
Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007.) (Proof shortened by Wolf Lammen, 19-Jul-2013.)
Hypotheses
Ref Expression
anim12ii.1  |-  ( ph  ->  ( ps  ->  ch ) )
anim12ii.2  |-  ( th 
->  ( ps  ->  ta ) )
Assertion
Ref Expression
anim12ii  |-  ( (
ph  /\  th )  ->  ( ps  ->  ( ch  /\  ta ) ) )

Proof of Theorem anim12ii
StepHypRef Expression
1 anim12ii.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21adantr 452 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 anim12ii.2 . . 3  |-  ( th 
->  ( ps  ->  ta ) )
43adantl 453 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ta ) )
52, 4jcad 520 1  |-  ( (
ph  /\  th )  ->  ( ps  ->  ( ch  /\  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  euim  2331  elex22  2967  tz7.2  4566  funcnvuni  5518  funressnfv  27968
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
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