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Metamath Proof Explorer

Theorem 3pm3.2i

Description: Infer conjunction of premises. (Contributed by NM, 10-Feb-1995)

Ref Expression
Hypotheses 3pm3.2i.1 
|- ph
3pm3.2i.2 
|- ps
3pm3.2i.3 
|- ch
Assertion 3pm3.2i 
|- ( ph /\ ps /\ ch )

Proof

Step Hyp Ref Expression
1 3pm3.2i.1 
 |-  ph
2 3pm3.2i.2 
 |-  ps
3 3pm3.2i.3 
 |-  ch
4 1 2 pm3.2i 
 |-  ( ph /\ ps )
5 df-3an 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
6 4 3 5 mpbir2an 
 |-  ( ph /\ ps /\ ch )