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Theorem pm2.61ddan 767
Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013.)
Hypotheses
Ref Expression
pm2.61ddan.1  |-  ( (
ph  /\  ps )  ->  th )
pm2.61ddan.2  |-  ( (
ph  /\  ch )  ->  th )
pm2.61ddan.3  |-  ( (
ph  /\  ( -.  ps  /\  -.  ch )
)  ->  th )
Assertion
Ref Expression
pm2.61ddan  |-  ( ph  ->  th )

Proof of Theorem pm2.61ddan
StepHypRef Expression
1 pm2.61ddan.1 . 2  |-  ( (
ph  /\  ps )  ->  th )
2 pm2.61ddan.2 . . . 4  |-  ( (
ph  /\  ch )  ->  th )
32adantlr 695 . . 3  |-  ( ( ( ph  /\  -.  ps )  /\  ch )  ->  th )
4 pm2.61ddan.3 . . . 4  |-  ( (
ph  /\  ( -.  ps  /\  -.  ch )
)  ->  th )
54anassrs 629 . . 3  |-  ( ( ( ph  /\  -.  ps )  /\  -.  ch )  ->  th )
63, 5pm2.61dan 766 . 2  |-  ( (
ph  /\  -.  ps )  ->  th )
71, 6pm2.61dan 766 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358
This theorem is referenced by:  lgsdir2  20567  cdlemg24  30877
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 177  df-an 360
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