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Theorem syland 291
Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)
Hypotheses
Ref Expression
syland.1  |-  ( ph  ->  ( ps  ->  ch ) )
syland.2  |-  ( ph  ->  ( ( ch  /\  th )  ->  ta )
)
Assertion
Ref Expression
syland  |-  ( ph  ->  ( ( ps  /\  th )  ->  ta )
)

Proof of Theorem syland
StepHypRef Expression
1 syland.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 syland.2 . . . 4  |-  ( ph  ->  ( ( ch  /\  th )  ->  ta )
)
32expd 256 . . 3  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
41, 3syld 45 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
54impd 252 1  |-  ( ph  ->  ( ( ps  /\  th )  ->  ta )
)
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 is referenced by:  sylan2d  292  syl2and  293  sylani  403  nn0seqcvgd  11733
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