Metamath Proof Explorer


Theorem 19.17

Description: Theorem 19.17 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Hypothesis 19.17.1
|- F/ x ps
Assertion 19.17
|- ( A. x ( ph <-> ps ) -> ( A. x ph <-> ps ) )

Proof

Step Hyp Ref Expression
1 19.17.1
 |-  F/ x ps
2 albi
 |-  ( A. x ( ph <-> ps ) -> ( A. x ph <-> A. x ps ) )
3 1 19.3
 |-  ( A. x ps <-> ps )
4 2 3 bitrdi
 |-  ( A. x ( ph <-> ps ) -> ( A. x ph <-> ps ) )