Theorem hbsb2e 1205

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 1203	. 2 |- ([y / x]ph -> A.x(x = y -> E.yph))
2		sb2 1177	. . 3 |- (A.x(x = y -> E.yph) -> [y / x]E.yph)
3	2	a5i 989	. 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 954   = wceq 956  E.wex 980  [wsbc 1170

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-11 967  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

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