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Theorem equid1ALT 32421
Description: Alternate proof of equid 1841 and equid1 32403 from older axioms ax-c7 32382, ax-c10 32383 and ax-c9 32387. (Contributed by NM, 10-Jan-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equid1ALT  |-  x  =  x

Proof of Theorem equid1ALT
StepHypRef Expression
1 ax-c9 32387 . . . . 5  |-  ( -. 
A. x  x  =  x  ->  ( -.  A. x  x  =  x  ->  ( x  =  x  ->  A. x  x  =  x )
) )
21pm2.43i 50 . . . 4  |-  ( -. 
A. x  x  =  x  ->  ( x  =  x  ->  A. x  x  =  x )
)
32alimi 1681 . . 3  |-  ( A. x  -.  A. x  x  =  x  ->  A. x
( x  =  x  ->  A. x  x  =  x ) )
4 ax-c10 32383 . . 3  |-  ( A. x ( x  =  x  ->  A. x  x  =  x )  ->  x  =  x )
53, 4syl 17 . 2  |-  ( A. x  -.  A. x  x  =  x  ->  x  =  x )
6 ax-c7 32382 . 2  |-  ( -. 
A. x  -.  A. x  x  =  x  ->  x  =  x )
75, 6pm2.61i 168 1  |-  x  =  x
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-c7 32382  ax-c10 32383  ax-c9 32387
This theorem is referenced by: (None)
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