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Metamath Proof Explorer

Theorem el3v

Description: If a proposition is implied by x e.V , y e. V and z e.V (which is true, see vex ), then it is true. Inference forms (with |- A e. V , |- B e.V and |- C e. V hypotheses) of the general theorems (proving |- ( ( A e. V /\ B e. W /\ C e. X ) -> assertions) may be superfluous. (Contributed by Peter Mazsa, 13-Oct-2018)

Ref Expression
Hypothesis el3v.1 
|- ( ( x e. _V /\ y e. _V /\ z e. _V ) -> ph )
Assertion el3v 
|- ph

Proof

Step Hyp Ref Expression
1 el3v.1 
 |-  ( ( x e. _V /\ y e. _V /\ z e. _V ) -> ph )
2 vex 
 |-  x e. _V
3 vex 
 |-  y e. _V
4 vex 
 |-  z e. _V
5 2 3 4 1 mp3an 
 |-  ph