Metamath Proof Explorer

Theorem pm14.18

Description: Theorem *14.18 in WhiteheadRussell p. 189. (Contributed by Andrew Salmon, 11-Jul-2011)

Ref Expression
Assertion pm14.18 
|- ( E! x ph -> ( A. x ps -> [. ( iota x ph ) / x ]. ps ) )

Proof

Step Hyp Ref Expression
1 iotaexeu 
 |-  ( E! x ph -> ( iota x ph ) e. _V )
2 spsbc 
 |-  ( ( iota x ph ) e. _V -> ( A. x ps -> [. ( iota x ph ) / x ]. ps ) )
3 1 2 syl 
 |-  ( E! x ph -> ( A. x ps -> [. ( iota x ph ) / x ]. ps ) )