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Metamath Proof Explorer

Theorem pm13.13b

Description: Theorem *13.13 in WhiteheadRussell p. 178 with different variable substitution. (Contributed by Andrew Salmon, 3-Jun-2011)

Ref Expression
Assertion pm13.13b 
|- ( ( [. A / x ]. ph /\ x = A ) -> ph )

Proof

Step Hyp Ref Expression
1 sbceq1a 
 |-  ( x = A -> ( ph <-> [. A / x ]. ph ) )
2 1 biimparc 
 |-  ( ( [. A / x ]. ph /\ x = A ) -> ph )