Theorem hbsb2e 1247

Description: Special case of a bound-variable hypothesis builder for substitution.

Assertion

Ref	Expression
hbsb2e	|- ([y / x]ph -> A.x[y / x]E.yph)

Proof of Theorem hbsb2e

Step	Hyp	Ref	Expression
1		sb4e 1245	. 2 |- ([y / x]ph -> A.x(x = y -> E.yph))
2		sb2 1219	. . 3 |- (A.x(x = y -> E.yph) -> [y / x]E.yph)
3	2	a5i 1030	. 2 |- (A.x(x = y -> E.yph) -> A.x[y / x]E.yph)
4	1, 3	syl 10	1 |- ([y / x]ph -> A.x[y / x]E.yph)

Syntax hints:   -> wi 3  A.wal 995   = wceq 997  E.wex 1021  [wsbc 1212

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1004  ax-11 1008  ax-4 1014  ax-5o 1016  ax-6o 1019  ax-9o 1164

This theorem depends on definitions:  df-bi 154  df-an 232  df-ex 1022  df-sb 1214

Copyright terms: Public domain