Metamath Proof Explorer


Theorem uun123

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis uun123.1
|- ( ( ph /\ ch /\ ps ) -> th )
Assertion uun123
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 uun123.1
 |-  ( ( ph /\ ch /\ ps ) -> th )
2 3ancomb
 |-  ( ( ph /\ ch /\ ps ) <-> ( ph /\ ps /\ ch ) )
3 2 1 sylbir
 |-  ( ( ph /\ ps /\ ch ) -> th )