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Metamath Proof Explorer

Theorem pm13.193

Description: Theorem *13.193 in WhiteheadRussell p. 179. (Contributed by Andrew Salmon, 3-Jun-2011)

Ref Expression
Assertion pm13.193 
|- ( ( ph /\ x = y ) <-> ( [ y / x ] ph /\ x = y ) )

Proof

Step Hyp Ref Expression
1 sbequ12 
 |-  ( x = y -> ( ph <-> [ y / x ] ph ) )
2 1 pm5.32ri 
 |-  ( ( ph /\ x = y ) <-> ( [ y / x ] ph /\ x = y ) )