Theorem bj-dtrucor 31988

Description: Remove dependency on ax-13 2234 from dtrucor 4827. (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-dtrucor.1	⊢ 𝑥 = 𝑦

Assertion

Ref	Expression
bj-dtrucor	⊢ 𝑥 ≠ 𝑦

Distinct variable group:   𝑥,𝑦

Proof of Theorem bj-dtrucor

Step	Hyp	Ref	Expression
1		bj-dtru 31985	. . 3 ⊢ ¬ ∀𝑥 𝑥 = 𝑦
2	1	pm2.21i 115	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝑥 ≠ 𝑦)
3		bj-dtrucor.1	. 2 ⊢ 𝑥 = 𝑦
4	2, 3	mpg 1715	1 ⊢ 𝑥 ≠ 𝑦

Syntax hints:  ∀wal 1473   ≠ wne 2780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-nul 4717  ax-pow 4769

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)