Theorem 2albii 1406

Description: Inference adding 2 universal quantifiers to both sides of an equivalence. (Contributed by NM, 9-Mar-1997.)

Hypothesis

Ref	Expression
albii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
2albii	⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑥∀𝑦𝜓)

Proof of Theorem 2albii

Step	Hyp	Ref	Expression
1		albii.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	albii 1405	. 2 ⊢ (∀𝑦𝜑 ↔ ∀𝑦𝜓)
3	2	albii 1405	1 ⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑥∀𝑦𝜓)

Syntax hints:   ↔ wb 104  ∀wal 1288

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  mor  1991  mo4f  2009  moanim  2023  2eu4  2042  ralcomf  2529  raliunxp  4590  cnvsym  4828  intasym  4829  intirr  4831  codir  4833  qfto  4834  dffun4  5039  dffun4f  5044  funcnveq  5090  fun11  5094  fununi  5095  mpt22eqb  5768  addnq0mo  7060  mulnq0mo  7061  addsrmo  7343  mulsrmo  7344