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Theorem 4cases 915
Description: Inference eliminating two antecedents from the four possible cases that result from their true/false combinations. (Contributed by NM, 25-Oct-2003.)
Hypotheses
Ref Expression
4cases.1  |-  ( (
ph  /\  ps )  ->  ch )
4cases.2  |-  ( (
ph  /\  -.  ps )  ->  ch )
4cases.3  |-  ( ( -.  ph  /\  ps )  ->  ch )
4cases.4  |-  ( ( -.  ph  /\  -.  ps )  ->  ch )
Assertion
Ref Expression
4cases  |-  ch

Proof of Theorem 4cases
StepHypRef Expression
1 4cases.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
2 4cases.3 . . 3  |-  ( ( -.  ph  /\  ps )  ->  ch )
31, 2pm2.61ian 765 . 2  |-  ( ps 
->  ch )
4 4cases.2 . . 3  |-  ( (
ph  /\  -.  ps )  ->  ch )
5 4cases.4 . . 3  |-  ( ( -.  ph  /\  -.  ps )  ->  ch )
64, 5pm2.61ian 765 . 2  |-  ( -. 
ps  ->  ch )
73, 6pm2.61i 156 1  |-  ch
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358
This theorem is referenced by:  4casesdan  916  ax11eq  2145  ax11el  2146  suc11reg  7336  axlowdimlem15  24656  cdleme27a  31178
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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