Theorem socnv 36237

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 6291	. 2 ⊢ (𝑅 Or 𝐴 ↔ ◡𝑅 Or 𝐴)
2	1	biimpi 219	1 ⊢ (𝑅 Or 𝐴 → ◡𝑅 Or 𝐴)

Syntax hints:   → wi 4   Or wor 5570  ^◡ccnv 5662

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-10 2176  ax-11 2192  ax-12 2213  ax-ext 2735  ax-sep 5258  ax-pr 5406

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3or 1104  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-nf 1814  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-ral 3080  df-rab 3417  df-v 3457  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4288  df-if 4489  df-sn 4591  df-pr 4593  df-op 4597  df-br 5111  df-opab 5175  df-po 5571  df-so 5572  df-cnv 5671

This theorem is referenced by: (None)