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Metamath Proof Explorer

Theorem 19.32v

Description: Version of 19.32 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020)

Ref Expression
Assertion 19.32v 
|- ( A. x ( ph \/ ps ) <-> ( ph \/ A. x ps ) )

Proof

Step Hyp Ref Expression
1 19.21v 
 |-  ( A. x ( -. ph -> ps ) <-> ( -. ph -> A. x ps ) )
2 df-or 
 |-  ( ( ph \/ ps ) <-> ( -. ph -> ps ) )
3 2 albii 
 |-  ( A. x ( ph \/ ps ) <-> A. x ( -. ph -> ps ) )
4 df-or 
 |-  ( ( ph \/ A. x ps ) <-> ( -. ph -> A. x ps ) )
5 1 3 4 3bitr4i 
 |-  ( A. x ( ph \/ ps ) <-> ( ph \/ A. x ps ) )