This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem sbtT

Description: A substitution into a theorem remains true. sbt with the existence of no virtual hypotheses for the hypothesis expressed as the empty virtual hypothesis collection. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis sbtT.1 
|- ( T. -> ph )
Assertion sbtT 
|- [ y / x ] ph

Proof

Step Hyp Ref Expression
1 sbtT.1 
 |-  ( T. -> ph )
2 1 mptru 
 |-  ph
3 2 sbt 
 |-  [ y / x ] ph