Theorem sbtT 42140

Description: A substitution into a theorem remains true. sbt 2072 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	⊢ (⊤ → 𝜑)

Assertion

Ref	Expression
sbtT	⊢ [𝑦 / 𝑥]𝜑

Proof of Theorem sbtT

Step	Hyp	Ref	Expression
1		sbtT.1	. . 3 ⊢ (⊤ → 𝜑)
2	1	mptru 1548	. 2 ⊢ 𝜑
3	2	sbt 2072	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:   → wi 4  ⊤wtru 1542  [wsb 2070

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801

This theorem depends on definitions:  df-bi 206  df-tru 1544  df-sb 2071

This theorem is referenced by: (None)