Theorem socnv 35726

Description: The converse of a strict ordering is still a strict ordering. (Contributed by Scott Fenton, 13-Jun-2018.)

Assertion

Ref	Expression
socnv	⊢ (𝑅 Or 𝐴 → ◡𝑅 Or 𝐴)

Proof of Theorem socnv

Step	Hyp	Ref	Expression
1		cnvso 6319	. 2 ⊢ (𝑅 Or 𝐴 ↔ ◡𝑅 Or 𝐴)
2	1	biimpi 216	1 ⊢ (𝑅 Or 𝐴 → ◡𝑅 Or 𝐴)

Syntax hints:   → wi 4   Or wor 5606  ^◡ccnv 5699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2158  ax-12 2178  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pr 5447

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3or 1088  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ne 2947  df-ral 3068  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-br 5167  df-opab 5229  df-po 5607  df-so 5608  df-cnv 5708

This theorem is referenced by: (None)