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Metamath Proof Explorer

Theorem iotasbc5

Description: Theorem *14.205 in WhiteheadRussell p. 190. (Contributed by Andrew Salmon, 11-Jul-2011)

Ref Expression
Assertion iotasbc5 
|- ( E! x ph -> ( [. ( iota x ph ) / y ]. ps <-> E. y ( y = ( iota x ph ) /\ ps ) ) )

Proof

Step Hyp Ref Expression
1 sbc5 
 |-  ( [. ( iota x ph ) / y ]. ps <-> E. y ( y = ( iota x ph ) /\ ps ) )
2 1 a1i 
 |-  ( E! x ph -> ( [. ( iota x ph ) / y ]. ps <-> E. y ( y = ( iota x ph ) /\ ps ) ) )