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Theorem uun111 31538
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
uun111.1  |-  ( (
ph  /\  ph  /\  ph )  ->  ps )
Assertion
Ref Expression
uun111  |-  ( ph  ->  ps )

Proof of Theorem uun111
StepHypRef Expression
1 3anass 969 . . 3  |-  ( (
ph  /\  ph  /\  ph ) 
<->  ( ph  /\  ( ph  /\  ph ) ) )
2 anabs5 807 . . 3  |-  ( (
ph  /\  ( ph  /\ 
ph ) )  <->  ( ph  /\ 
ph ) )
3 anidm 644 . . 3  |-  ( (
ph  /\  ph )  <->  ph )
41, 2, 33bitri 271 . 2  |-  ( (
ph  /\  ph  /\  ph ) 
<-> 
ph )
5 uun111.1 . 2  |-  ( (
ph  /\  ph  /\  ph )  ->  ps )
64, 5sylbir 213 1  |-  ( ph  ->  ps )
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: (None)
  Copyright terms: Public domain W3C validator