Theorem rr2sscn2 39582

Description: ℝ^ 2 is a subset of CC^ 2. Common case. (Contributed by Glauco Siliprandi, 3-Mar-2021.)

Assertion

Ref	Expression
rr2sscn2	|- ( RR X. RR ) C_ ( CC X. CC )

Proof of Theorem rr2sscn2

Step	Hyp	Ref	Expression
1		ax-resscn 9993	. 2 |- RR C_ CC
2		xpss12 5225	. 2 |- ( ( RR C_ CC /\ RR C_ CC ) -> ( RR X. RR ) C_ ( CC X. CC ) )
3	1, 1, 2	mp2an 708	1 |- ( RR X. RR ) C_ ( CC X. CC )

Syntax hints:   C_ wss 3574   X. cxp 5112   CCcc 9934   RRcr 9935

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-resscn 9993

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-in 3581  df-ss 3588  df-opab 4713  df-xp 5120

This theorem is referenced by:  ovolval2lem  40857  ovolval2  40858  ovolval3  40861