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Axiom ax-pre-mulext 6801
Description: Strong extensionality of multiplication (expressed in terms of  <RR). Axiom for real and complex numbers, justified by theorem axpre-mulext 6772

(Contributed by Jim Kingdon, 18-Feb-2020.)

Assertion
Ref Expression
ax-pre-mulext  RR  RR  C  RR  x.  C  <RR  x.  C  <RR  <RR

Detailed syntax breakdown of Axiom ax-pre-mulext
StepHypRef Expression
1 cA . . . 4
2 cr 6710 . . . 4  RR
31, 2wcel 1390 . . 3  RR
4 cB . . . 4
54, 2wcel 1390 . . 3  RR
6 cC . . . 4  C
76, 2wcel 1390 . . 3  C  RR
83, 5, 7w3a 884 . 2  RR  RR  C  RR
9 cmul 6716 . . . . 5  x.
101, 6, 9co 5455 . . . 4  x.  C
114, 6, 9co 5455 . . . 4  x.  C
12 cltrr 6715 . . . 4  <RR
1310, 11, 12wbr 3755 . . 3  x.  C  <RR  x.  C
141, 4, 12wbr 3755 . . . 4  <RR
154, 1, 12wbr 3755 . . . 4  <RR
1614, 15wo 628 . . 3  <RR  <RR
1713, 16wi 4 . 2  x.  C  <RR  x.  C  <RR  <RR
188, 17wi 4 1  RR  RR  C  RR  x.  C  <RR  x.  C  <RR  <RR
Colors of variables: wff set class
This axiom is referenced by:  remulext1  7383
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