Theorem sbtT 38783

Description: A substitution into a theorem remains true. sbt 2419 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.)

Hypothesis

Ref	Expression
sbtT.1	|- ( T. -> ph )

Assertion

Ref	Expression
sbtT	|- [ y / x ] ph

Proof of Theorem sbtT

Step	Hyp	Ref	Expression
1		sbtT.1	. . 3 |- ( T. -> ph )
2	1	trud 1493	. 2 |- ph
3	2	sbt 2419	1 |- [ y / x ] ph

Syntax hints:   -> wi 4   T. wtru 1484   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)