Theorem socnv 35999

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 6246	. 2 ⊢ (𝑅 Or 𝐴 ↔ ◡𝑅 Or 𝐴)
2	1	biimpi 217	1 ⊢ (𝑅 Or 𝐴 → ◡𝑅 Or 𝐴)

Syntax hints:   → wi 4   Or wor 5532  ^◡ccnv 5624

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-10 2152  ax-11 2168  ax-12 2189  ax-ext 2712  ax-sep 5225  ax-pr 5369

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3or 1093  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-ne 2936  df-ral 3055  df-rab 3393  df-v 3434  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4269  df-if 4462  df-sn 4563  df-pr 4565  df-op 4569  df-br 5080  df-opab 5142  df-po 5533  df-so 5534  df-cnv 5633

This theorem is referenced by: (None)