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Theorem syl2im 38
Description: Replace two antecedents. Implication-only version of syl2an 283. (Contributed by Wolf Lammen, 14-May-2013.)
Hypotheses
Ref Expression
syl2im.1  |-  ( ph  ->  ps )
syl2im.2  |-  ( ch 
->  th )
syl2im.3  |-  ( ps 
->  ( th  ->  ta ) )
Assertion
Ref Expression
syl2im  |-  ( ph  ->  ( ch  ->  ta ) )

Proof of Theorem syl2im
StepHypRef Expression
1 syl2im.1 . 2  |-  ( ph  ->  ps )
2 syl2im.2 . . 3  |-  ( ch 
->  th )
3 syl2im.3 . . 3  |-  ( ps 
->  ( th  ->  ta ) )
42, 3syl5 32 . 2  |-  ( ps 
->  ( ch  ->  ta ) )
51, 4syl 14 1  |-  ( ph  ->  ( ch  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  sylc  61  bi3ant  222  pm3.12dc  900  pm3.13dc  901  nfrimi  1459  vtoclr  4434  funopg  4984  xpiderm  6264  ixxssixx  9053  difelfzle  9274  bj-inf2vnlem1  11032
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