Theorem pw1ss1c 4158

Description: A unit power class is a subset of 1_c. (Contributed by SF, 22-Jan-2015.)

Assertion

Ref	Expression
pw1ss1c	⊢ ℘1A ⊆ 1c

Proof of Theorem pw1ss1c

Step	Hyp	Ref	Expression
1		df-pw1 4137	. 2 ⊢ ℘1A = (℘A ∩ 1c)
2		inss2 3476	. 2 ⊢ (℘A ∩ 1c) ⊆ 1c
3	1, 2	eqsstri 3301	1 ⊢ ℘1A ⊆ 1c

Syntax hints:   ∩ cin 3208   ⊆ wss 3257  ℘cpw 3722  1_cc1c 4134  ℘₁cpw1 4135

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pw1 4137

This theorem is referenced by:  eqpw1  4162  pw111  4170  eqpw1uni  4330  pw1equn  4331  pw1eqadj  4332  sspw1  4335  sspw12  4336  enpw1pw  6075  ce0lenc1  6239  tlenc1c  6240