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Theorem eel2122old 31762
Description: el2122old 31763 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel2122old.1  |-  ( (
ph  /\  ps )  ->  ch )
eel2122old.2  |-  ( ps 
->  th )
eel2122old.3  |-  ( ps 
->  ta )
eel2122old.4  |-  ( ( ch  /\  th  /\  ta )  ->  et )
Assertion
Ref Expression
eel2122old  |-  ( (
ph  /\  ps )  ->  et )

Proof of Theorem eel2122old
StepHypRef Expression
1 eel2122old.3 . . . . . 6  |-  ( ps 
->  ta )
2 eel2122old.2 . . . . . . 7  |-  ( ps 
->  th )
3 eel2122old.1 . . . . . . . 8  |-  ( (
ph  /\  ps )  ->  ch )
4 eel2122old.4 . . . . . . . . 9  |-  ( ( ch  /\  th  /\  ta )  ->  et )
543exp 1187 . . . . . . . 8  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
63, 5syl 16 . . . . . . 7  |-  ( (
ph  /\  ps )  ->  ( th  ->  ( ta  ->  et ) ) )
72, 6syl5 32 . . . . . 6  |-  ( (
ph  /\  ps )  ->  ( ps  ->  ( ta  ->  et ) ) )
81, 7syl7 68 . . . . 5  |-  ( (
ph  /\  ps )  ->  ( ps  ->  ( ps  ->  et ) ) )
98ex 434 . . . 4  |-  ( ph  ->  ( ps  ->  ( ps  ->  ( ps  ->  et ) ) ) )
109pm2.43d 48 . . 3  |-  ( ph  ->  ( ps  ->  ( ps  ->  et ) ) )
1110pm2.43d 48 . 2  |-  ( ph  ->  ( ps  ->  et ) )
1211imp 429 1  |-  ( (
ph  /\  ps )  ->  et )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967
This theorem is referenced by:  el2122old  31763  suctrALTcf  31971
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