Theorem socnv 36078

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 6271	. 2 ⊢ (𝑅 Or 𝐴 ↔ ◡𝑅 Or 𝐴)
2	1	biimpi 218	1 ⊢ (𝑅 Or 𝐴 → ◡𝑅 Or 𝐴)

Syntax hints:   → wi 4   Or wor 5552  ^◡ccnv 5644

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-10 2174  ax-11 2190  ax-12 2211  ax-ext 2733  ax-sep 5245  ax-pr 5389

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3or 1098  df-3an 1099  df-tru 1562  df-fal 1572  df-ex 1799  df-nf 1803  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-ral 3076  df-rab 3414  df-v 3455  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4480  df-sn 4582  df-pr 4584  df-op 4588  df-br 5100  df-opab 5162  df-po 5553  df-so 5554  df-cnv 5653

This theorem is referenced by: (None)