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Theorem un01 28878
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 1312 . . . 4  |-  T.
21jctl 525 . . 3  |-  ( ph  ->  (  T.  /\  ph ) )
3 un01.1 . . . 4  |-  (. (.  T.  ,. ph ).  ->.  ps ).
43dfvd2ani 28651 . . 3  |-  ( (  T.  /\  ph )  ->  ps )
52, 4syl 15 . 2  |-  ( ph  ->  ps )
65dfvd1ir 28640 1  |-  (. ph  ->.  ps
).
Colors of variables: wff set class
Syntax hints:    /\ wa 358    T. wtru 1307   (.wvd1 28636   (.wvhc2 28648
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 28637  df-vhc2 28649
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