Theorem sbt 1190

Description: A substitution into a theorem remains true. (See chvar 1165 and chvarv 1325 for versions with implicit substitution.

Hypothesis

Ref	Expression
sbt.1	|- ph

Assertion

Ref	Expression
sbt	|- [y / x]ph

Proof of Theorem sbt

Step	Hyp	Ref	Expression
1		sb2 1175	. 2 |- (A.x(x = y -> ph) -> [y / x]ph)
2		sbt.1	. . 3 |- ph
3	2	a1i 8	. 2 |- (x = y -> ph)
4	1, 3	mpg 984	1 |- [y / x]ph

Syntax hints:   -> wi 3  [wsbc 1168

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170

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