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Theorem axlmp3 25129
Description: Moving a universal quantifier inside and outside a box. (Contributed by FL, 16-Sep-2016.)
Hypothesis
Ref Expression
axlmp3.1  |-  [.] A. x ph
Assertion
Ref Expression
axlmp3  |-  A. x [.] ph

Proof of Theorem axlmp3
StepHypRef Expression
1 axlmp3.1 . . . . 5  |-  [.] A. x ph
21axlmp1 25127 . . . 4  |-  A. x ph
32spi 1750 . . 3  |-  ph
43ax-lmp 25081 . 2  |-  [.] ph
54ax-gen 1536 1  |-  A. x [.] ph
Colors of variables: wff set class
Syntax hints:   A.wal 1530   [.]wbox 25073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ltl1 25077  ax-ltl2 25078  ax-ltl3 25079  ax-ltl4 25080  ax-lmp 25081  ax-nmp 25082  ax-ltl5 25096  ax-ltl6 25097
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 25083
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