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Metamath Proof Explorer

Theorem 19.31

Description: Theorem 19.31 of Margaris p. 90. See 19.31v for a version requiring fewer axioms. (Contributed by NM, 14-May-1993)

Ref Expression
Hypothesis 19.31.1 
|- F/ x ps
Assertion 19.31 
|- ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )

Proof

Step Hyp Ref Expression
1 19.31.1 
 |-  F/ x ps
2 1 19.32 
 |-  ( A. x ( ps \/ ph ) <-> ( ps \/ A. x ph ) )
3 orcom 
 |-  ( ( ph \/ ps ) <-> ( ps \/ ph ) )
4 3 albii 
 |-  ( A. x ( ph \/ ps ) <-> A. x ( ps \/ ph ) )
5 orcom 
 |-  ( ( A. x ph \/ ps ) <-> ( ps \/ A. x ph ) )
6 2 4 5 3bitr4i 
 |-  ( A. x ( ph \/ ps ) <-> ( A. x ph \/ ps ) )