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Axiom ax-ltl1 25077
Description: If  ( ph  ->  ps ) and  ph always hold then  ps always holds. (Contributed by FL, 22-Feb-2011.)
Assertion
Ref Expression
ax-ltl1  |-  ( [.] ( ph  ->  ps )  ->  ( [.] ph  ->  [.] ps ) )

Detailed syntax breakdown of Axiom ax-ltl1
StepHypRef Expression
1 wph . . . 4  wff  ph
2 wps . . . 4  wff  ps
31, 2wi 4 . . 3  wff  ( ph  ->  ps )
43wbox 25073 . 2  wff  [.] ( ph  ->  ps )
51wbox 25073 . . 3  wff  [.] ph
62wbox 25073 . . 3  wff  [.] ps
75, 6wi 4 . 2  wff  ( [.] ph  ->  [.] ps )
84, 7wi 4 1  wff  ( [.] ( ph  ->  ps )  ->  ( [.] ph  ->  [.] ps ) )
Colors of variables: wff set class
This axiom is referenced by:  impbox  25084  impbox2  25108  boximd  25111
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