Theorem pssned 4051

Description: Proper subclasses are unequal. Deduction form of pssne 4049. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
pssssd.1	⊢ (𝜑 → 𝐴 ⊊ 𝐵)

Assertion

Ref	Expression
pssned	⊢ (𝜑 → 𝐴 ≠ 𝐵)

Proof of Theorem pssned

Step	Hyp	Ref	Expression
1		pssssd.1	. 2 ⊢ (𝜑 → 𝐴 ⊊ 𝐵)
2		pssne 4049	. 2 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝐴 ≠ 𝐵)

Syntax hints:   → wi 4   ≠ wne 2928   ⊊ wpss 3903

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-pss 3922

This theorem is referenced by:  omsucne  7815  ackbij1lem15  10121  canthnumlem  10536  canthp1lem2  10541  mrieqv2d  17542  slwpss  19522  hashpss  32786  topdifinffinlem  37380  lsatssn0  39040  islshpcv  39091  lkrpssN  39201