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Theorem axlmp1 25127
Description: If  ph always holds, then it is a theorem. (Contributed by FL, 16-Sep-2016.)
Hypothesis
Ref Expression
axlmp1.1  |-  [.] ph
Assertion
Ref Expression
axlmp1  |-  ph

Proof of Theorem axlmp1
StepHypRef Expression
1 axlmp1.1 . 2  |-  [.] ph
2 alneal1 25103 . 2  |-  ( [.] ph  ->  ph )
31, 2ax-mp 8 1  |-  ph
Colors of variables: wff set class
Syntax hints:   [.]wbox 25073
This theorem is referenced by:  axlmp2  25128  axlmp3  25129
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  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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