Metamath Proof Explorer

Theorem pm10.14

Description: Theorem *10.14 in WhiteheadRussell p. 146. (Contributed by Andrew Salmon, 17-Jun-2011)

Ref Expression
Assertion pm10.14 
|- ( ( A. x ph /\ A. x ps ) -> ( [ y / x ] ph /\ [ y / x ] ps ) )

Proof

Step Hyp Ref Expression
1 stdpc4 
 |-  ( A. x ph -> [ y / x ] ph )
2 stdpc4 
 |-  ( A. x ps -> [ y / x ] ps )
3 1 2 anim12i 
 |-  ( ( A. x ph /\ A. x ps ) -> ( [ y / x ] ph /\ [ y / x ] ps ) )