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Theorem un01 28802
Description: A unionizing deduction (Contributed by Alan Sare, 28-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
un01.1  |-  (. (.  T.  ,. ph ).  ->.  ps ).
Assertion
Ref Expression
un01  |-  (. ph  ->.  ps
).

Proof of Theorem un01
StepHypRef Expression
1 tru 1330 . . . 4  |-  T.
21jctl 526 . . 3  |-  ( ph  ->  (  T.  /\  ph ) )
3 un01.1 . . . 4  |-  (. (.  T.  ,. ph ).  ->.  ps ).
43dfvd2ani 28576 . . 3  |-  ( (  T.  /\  ph )  ->  ps )
52, 4syl 16 . 2  |-  ( ph  ->  ps )
65dfvd1ir 28565 1  |-  (. ph  ->.  ps
).
Colors of variables: wff set class
Syntax hints:    /\ wa 359    T. wtru 1325   (.wvd1 28561   (.wvhc2 28573
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 178  df-an 361  df-tru 1328  df-vd1 28562  df-vhc2 28574
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