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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	⊢ ( ⊤ → 𝜑 )
	Assertion	sbtT	⊢ [ 𝑦 / 𝑥 ] 𝜑

Proof

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