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Theorem rexbidvALT 2937
Description: Alternative, shorter proof of rexbidv 2936, using more axioms. (Contributed by NM, 20-Nov-1994.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
rexbidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
rexbidvALT  |-  ( ph  ->  ( E. x  e.  A  ps  <->  E. x  e.  A  ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem rexbidvALT
StepHypRef Expression
1 nfv 1755 . 2  |-  F/ x ph
2 rexbidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2rexbid 2935 1  |-  ( ph  ->  ( E. x  e.  A  ps  <->  E. x  e.  A  ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   E.wrex 2772
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-rex 2777
This theorem is referenced by: (None)
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