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Theorem uun121 37031
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
uun121.1  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
Assertion
Ref Expression
uun121  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem uun121
StepHypRef Expression
1 anabs5 816 . 2  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )
2 uun121.1 . 2  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
31, 2sylbir 216 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370
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 188  df-an 372
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator