Metamath Proof Explorer

Theorem 2al2imi

Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Hypothesis 2al2imi.1 
|- ( ph -> ( ps -> ch ) )
Assertion 2al2imi 
|- ( A. x A. y ph -> ( A. x A. y ps -> A. x A. y ch ) )

Proof

Step Hyp Ref Expression
1 2al2imi.1 
 |-  ( ph -> ( ps -> ch ) )
2 1 al2imi 
 |-  ( A. y ph -> ( A. y ps -> A. y ch ) )
3 2 al2imi 
 |-  ( A. x A. y ph -> ( A. x A. y ps -> A. x A. y ch ) )