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Theorem eel000cT 31724
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel000cT.1  |-  ph
eel000cT.2  |-  ps
eel000cT.3  |-  ch
eel000cT.4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
eel000cT  |-  ( T. 
->  th )

Proof of Theorem eel000cT
StepHypRef Expression
1 eel000cT.3 . . 3  |-  ch
2 eel000cT.2 . . . 4  |-  ps
3 eel000cT.1 . . . . 5  |-  ph
4 eel000cT.4 . . . . 5  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
53, 4mp3an1 1302 . . . 4  |-  ( ( ps  /\  ch )  ->  th )
62, 5mpan 670 . . 3  |-  ( ch 
->  th )
71, 6ax-mp 5 . 2  |-  th
87a1i 11 1  |-  ( T. 
->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 965   T. wtru 1371
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: (None)
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