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Theorem anim12ii 570
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 465 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 anim12ii.2 . . 3  |-  ( th 
->  ( ps  ->  ta ) )
43adantl 466 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ta ) )
52, 4jcad 533 1  |-  ( (
ph  /\  th )  ->  ( ps  ->  ( ch  /\  ta ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  euim  2333  2mo  2369  elex22  3091  tz7.2  4815  funcnvuni  6643  funressnfv  30202
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