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Metamath Proof Explorer

Theorem bianass

Description: An inference to merge two lists of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019)

Ref Expression
Hypothesis bianass.1 
|- ( ph <-> ( ps /\ ch ) )
Assertion bianass 
|- ( ( et /\ ph ) <-> ( ( et /\ ps ) /\ ch ) )

Proof

Step Hyp Ref Expression
1 bianass.1 
 |-  ( ph <-> ( ps /\ ch ) )
2 1 anbi2i 
 |-  ( ( et /\ ph ) <-> ( et /\ ( ps /\ ch ) ) )
3 anass 
 |-  ( ( ( et /\ ps ) /\ ch ) <-> ( et /\ ( ps /\ ch ) ) )
4 2 3 bitr4i 
 |-  ( ( et /\ ph ) <-> ( ( et /\ ps ) /\ ch ) )