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Theorem un10 28563
Description: A unionizing deduction (Contributed by Alan Sare, 28-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
un10.1  |-  (. (. ph ,.  T.  ).  ->.  ps ).
Assertion
Ref Expression
un10  |-  (. ph  ->.  ps
).

Proof of Theorem un10
StepHypRef Expression
1 tru 1312 . . . 4  |-  T.
21jctr 526 . . 3  |-  ( ph  ->  ( ph  /\  T.  ) )
3 un10.1 . . . 4  |-  (. (. ph ,.  T.  ).  ->.  ps ).
43dfvd2ani 28352 . . 3  |-  ( (
ph  /\  T.  )  ->  ps )
52, 4syl 15 . 2  |-  ( ph  ->  ps )
65dfvd1ir 28341 1  |-  (. ph  ->.  ps
).
Colors of variables: wff set class
Syntax hints:    /\ wa 358    T. wtru 1307   (.wvd1 28337   (.wvhc2 28349
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-tru 1310  df-vd1 28338  df-vhc2 28350
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