Metamath Proof Explorer


Theorem barocoALT

Description: Alternate proof of festino , shorter but using more axioms. See comment of dariiALT . (Contributed by David A. Wheeler, 27-Aug-2016) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses baroco.maj
|- A. x ( ph -> ps )
baroco.min
|- E. x ( ch /\ -. ps )
Assertion barocoALT
|- E. x ( ch /\ -. ph )

Proof

Step Hyp Ref Expression
1 baroco.maj
 |-  A. x ( ph -> ps )
2 baroco.min
 |-  E. x ( ch /\ -. ps )
3 1 spi
 |-  ( ph -> ps )
4 3 con3i
 |-  ( -. ps -> -. ph )
5 4 anim2i
 |-  ( ( ch /\ -. ps ) -> ( ch /\ -. ph ) )
6 2 5 eximii
 |-  E. x ( ch /\ -. ph )