Theorem sbt 1192

Description: A substitution into a theorem remains true. (See chvar 1167 and chvarv 1327 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 1177	. 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 986	1 |- [y / x]ph

Syntax hints:   -> wi 3  [wsbc 1170

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172

Copyright terms: Public domain