Theorem sbt 899

Description: A substitution into a theorem remains true. (See chv2 850 and chv 984 for versions with implicit substitution.

Hypothesis

Ref	Expression
sbt.1	⊢ φ

Assertion

Ref	Expression
sbt	⊢ [y / x]φ

Proof of Theorem sbt

Step	Hyp	Ref	Expression
1		sb2 859	. 2 ⊢ (∀x(x = y → φ) → [y / x]φ)
2		sbt.1	. . 3 ⊢ φ
3	2	a1i 7	. 2 ⊢ (x = y → φ)
4	1, 3	mpg 684	1 ⊢ [y / x]φ

Syntax hints:   → wi 2   = weq 797  [wsb 852

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853

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