Theorem alne 14326

Description: If ph always holds, it holds in the next step.

Assertion

Ref	Expression
alne	|- ([.]ph -> ()ph)

Proof of Theorem alne

Step	Hyp	Ref	Expression
1		alneal2 14325	. 2 |- ([.]ph -> ()[.]ph)
2		alneal1 14324	. . 3 |- ([.]ph -> ph)
3	2	impxt 14310	. 2 |- (()[.]ph -> ()ph)
4	1, 3	syl 12	1 |- ([.]ph -> ()ph)

Syntax hints:   -> wi 3  [.]wbox 14297  ()wcirc 14299

This theorem is referenced by:  althalne 14329

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-ltl1 14301  ax-ltl2 14302  ax-ltl3 14303  ax-ltl4 14304  ax-lmp 14305  ax-nmp 14306  ax-ltl5 14318  ax-ltl6 14319

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-tru 1262  df-dia 14307

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