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Theorem e1111 36465
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 6-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e1111.1  |-  (. ph  ->.  ps
).
e1111.2  |-  (. ph  ->.  ch
).
e1111.3  |-  (. ph  ->.  th
).
e1111.4  |-  (. ph  ->.  ta
).
e1111.5  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  et ) ) ) )
Assertion
Ref Expression
e1111  |-  (. ph  ->.  et
).

Proof of Theorem e1111
StepHypRef Expression
1 e1111.1 . . . 4  |-  (. ph  ->.  ps
).
21in1 36352 . . 3  |-  ( ph  ->  ps )
3 e1111.2 . . . 4  |-  (. ph  ->.  ch
).
43in1 36352 . . 3  |-  ( ph  ->  ch )
5 e1111.3 . . . 4  |-  (. ph  ->.  th
).
65in1 36352 . . 3  |-  ( ph  ->  th )
7 e1111.4 . . . 4  |-  (. ph  ->.  ta
).
87in1 36352 . . 3  |-  ( ph  ->  ta )
9 e1111.5 . . 3  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  et ) ) ) )
102, 4, 6, 8, 9ee1111 36283 . 2  |-  ( ph  ->  et )
1110dfvd1ir 36354 1  |-  (. ph  ->.  et
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36350
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-vd1 36351
This theorem is referenced by:  trsbcVD  36688
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