Theorem hbsb2e 1204

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 1202	. 2 |- ([y / x]ph -> A.x(x = y -> E.yph))
2		sb2 1176	. . 3 |- (A.x(x = y -> E.yph) -> [y / x]E.yph)
3	2	a5i 988	. 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 953   = wceq 955  E.wex 979  [wsbc 1169

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-11 966  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171

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