Theorem ra4sbca 1969

Description: Restricted quantifier version of Axiom 4 of [Mendelson] p. 69.

Assertion

Ref	Expression
ra4sbca	|- ((A e. B /\ A.x e. B ph) -> [A / x]ph)

Distinct variable group:   x,B

Proof of Theorem ra4sbca

Step	Hyp	Ref	Expression
1		ra4sbc 1968	. 2 |- (A e. B -> (A.x e. B ph -> [A / x]ph))
2	1	imp 350	1 |- ((A e. B /\ A.x e. B ph) -> [A / x]ph)

Syntax hints:   -> wi 3   /\ wa 223   e. wcel 1105  [wsbc 1153  A.wral 1621

This theorem is referenced by:  fsump1s 6902  fsumcmp 6929

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955  ax-8 1101  ax-9 1102  ax-10 1103  ax-12 1104  ax-11 1180  ax-17 1190  ax-16 1194  ax-11o 1202  ax-ext 1436

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 957  df-sb 1155  df-clab 1441  df-cleq 1446  df-clel 1449  df-ral 1625  df-v 1787  df-sbc 1913

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