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Theorem 3impdirp1 28905
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. 3impdir 1238 is ~? uun3132 and is in set.mm. 3impdirp1 28905 is ~? uun3132p1. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
3impdirp1.1  |-  ( ( ( ch  /\  ps )  /\  ( ph  /\  ps ) )  ->  th )
Assertion
Ref Expression
3impdirp1  |-  ( (
ph  /\  ch  /\  ps )  ->  th )

Proof of Theorem 3impdirp1
StepHypRef Expression
1 ancom 437 . . 3  |-  ( ( ( ch  /\  ps )  /\  ( ph  /\  ps ) )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  ps )
) )
2 3impdirp1.1 . . 3  |-  ( ( ( ch  /\  ps )  /\  ( ph  /\  ps ) )  ->  th )
31, 2sylbir 204 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ps ) )  ->  th )
433impdir 1238 1  |-  ( (
ph  /\  ch  /\  ps )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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