Theorem bnj1079 12906

Description: First-order logic and set theory.

Hypotheses

Ref	Expression
bnj1079.1	|- E.x(ph -> ps)
bnj1079.2	|- (ph <-> ph')

Assertion

Ref	Expression
bnj1079	|- E.x(ph' -> ps)

Proof of Theorem bnj1079

Step	Hyp	Ref	Expression
1		bnj1079.1	. 2 |- E.x(ph -> ps)
2		bnj1079.2	. . . 4 |- (ph <-> ph')
3	2	imbi1i 203	. . 3 |- ((ph -> ps) <-> (ph' -> ps))
4	3	exbii 1398	. 2 |- (E.x(ph -> ps) <-> E.x(ph' -> ps))
5	1, 4	mpbi 206	1 |- E.x(ph' -> ps)

Syntax hints:   -> wi 3   <-> wb 163  E.wex 1326

This theorem is referenced by:  bnj1062 13397  bnj1080 13406  bnj1145 13431

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

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

Copyright terms: Public domain