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Metamath Proof Explorer

Theorem 1t1e1ALT

Description: Alternate proof of 1t1e1 using a different set of axioms (add ax-mulrcl , ax-i2m1 , ax-1ne0 , ax-rrecex and remove ax-resscn , ax-mulcom , ax-mulass , ax-distr ). (Contributed by Steven Nguyen, 20-Sep-2022) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 1t1e1ALT 
|- ( 1 x. 1 ) = 1

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 ax-1rid 
 |-  ( 1 e. RR -> ( 1 x. 1 ) = 1 )
3 1 2 ax-mp 
 |-  ( 1 x. 1 ) = 1