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Theorem syl6com 35
Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005.)
Hypotheses
Ref Expression
syl6com.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl6com.2  |-  ( ch 
->  th )
Assertion
Ref Expression
syl6com  |-  ( ps 
->  ( ph  ->  th )
)

Proof of Theorem syl6com
StepHypRef Expression
1 syl6com.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 syl6com.2 . . 3  |-  ( ch 
->  th )
31, 2syl6 33 . 2  |-  ( ph  ->  ( ps  ->  th )
)
43com12 30 1  |-  ( ps 
->  ( ph  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  pclem6  1356  spimh  1717  ax16  1793  ax16i  1838  elres  4902  funcnvuni  5239  funrnex  6062  negf1o  8257  basis2  12457  bj-inf2vnlem2  13557
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