Theorem a4sbce-2 16333

Description: Theorem *11.36 in [WhiteheadRussell] p. 162.

Assertion

Ref	Expression
a4sbce-2	|- ([z / x][w / y]ph -> E.xE.yph)

Proof of Theorem a4sbce-2

Step	Hyp	Ref	Expression
1		a4sbe 1613	. 2 |- ([z / x][w / y]ph -> E.x[w / y]ph)
2		a4sbe 1613	. . 3 |- ([w / y]ph -> E.yph)
3	2	eximi 1387	. 2 |- (E.x[w / y]ph -> E.xE.yph)
4	1, 3	syl 12	1 |- ([z / x][w / y]ph -> E.xE.yph)

Syntax hints:   -> wi 3  E.wex 1326  [wsbc 1534

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-10 1308  ax-12 1310  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-11o 1588

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536

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