Theorem a4sbe 1243

Description: A specialization theorem.

Assertion

Ref	Expression
a4sbe	|- ([y / x]ph -> E.xph)

Proof of Theorem a4sbe

Step	Hyp	Ref	Expression
1		stdpc4 1185	. . . 4 |- (A.x -. ph -> [y / x] -. ph)
2		sbn 1231	. . . 4 |- ([y / x] -. ph <-> -. [y / x]ph)
3	1, 2	sylib 198	. . 3 |- (A.x -. ph -> -. [y / x]ph)
4	3	con2i 97	. 2 |- ([y / x]ph -> -. A.x -. ph)
5		df-ex 981	. 2 |- (E.xph <-> -. A.x -. ph)
6	4, 5	sylibr 200	1 |- ([y / x]ph -> E.xph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 954  E.wex 980  [wsbc 1170

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172

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