Theorem lerel 11207

Description: "Less than or equal to" is a relation. (Contributed by FL, 2-Aug-2009.) (Revised by Mario Carneiro, 28-Apr-2015.)

Assertion

Ref	Expression
lerel	⊢ Rel ≤

Proof of Theorem lerel

Step	Hyp	Ref	Expression
1		lerelxr 11206	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5643	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5732	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3890   × cxp 5623  Rel wrel 5630  ℝ^*cxr 11176   ≤ cle 11178

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-dif 3893  df-ss 3907  df-opab 5142  df-xp 5631  df-rel 5632  df-le 11183

This theorem is referenced by:  dfle2  13096  dflt2  13097  ledm  18554  lern  18555  lefld  18556  letsr  18557  dvle  25999  gtiso  32800