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Theorem un10 31823
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 1374 . . . 4  |- T.
21jctr 542 . . 3  |-  ( ph  ->  ( ph  /\ T.  ) )
3 un10.1 . . . 4  |-  (. (. ph ,. T.  ).  ->.  ps ).
43dfvd2ani 31598 . . 3  |-  ( (
ph  /\ T.  )  ->  ps )
52, 4syl 16 . 2  |-  ( ph  ->  ps )
65dfvd1ir 31588 1  |-  (. ph  ->.  ps
).
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369   T. wtru 1371   (.wvd1 31584   (.wvhc2 31595
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 185  df-an 371  df-tru 1373  df-vd1 31585  df-vhc2 31596
This theorem is referenced by: (None)
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