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Theorem axlmp1 24436
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 24412 . 2  |-  ( [.] ph  ->  ph )
31, 2ax-mp 8 1  |-  ph
Colors of variables: wff set class
Syntax hints:   [.]wbox 24382
This theorem is referenced by:  axlmp2  24437  axlmp3  24438
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 24386  ax-ltl2 24387  ax-ltl3 24388  ax-ltl4 24389  ax-lmp 24390  ax-nmp 24391  ax-ltl5 24405  ax-ltl6 24406
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 24392
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