Theorem suball-P7r.RC 1041

Description: Inference Form of suball-P7r 1039. †

This is the restatement of a previously proven result. Do not use in proofs. Use suball-P7.RC 974 instead.

Hypothesis

Ref	Expression
suball-P7r.RC.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
suball-P7r.RC	⊢ (∀𝑥𝜑 ↔ ∀𝑥𝜓)

Proof of Theorem suball-P7r.RC

Step	Hyp	Ref	Expression
1		suball-P7r.RC.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2	1	suball-P7.RC 974	1 ⊢ (∀𝑥𝜑 ↔ ∀𝑥𝜓)

Syntax hints:  ∀wff-forall 8   ↔ wff-bi 104

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17  ax-L6 18  ax-L7 19  ax-L10 27  ax-L11 28  ax-L12 29

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596  df-nfree-D6.1 682  df-psub-D6.2 716

This theorem is referenced by: (None)