Theorem 3albii 1821

Description: Inference adding three universal quantifiers to both sides of an equivalence. (Contributed by Peter Mazsa, 10-Aug-2018.)

Hypothesis

Ref	Expression
albii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
3albii	⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑥∀𝑦∀𝑧𝜓)

Proof of Theorem 3albii

Step	Hyp	Ref	Expression
1		albii.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	2albii 1820	. 2 ⊢ (∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧𝜓)
3	2	albii 1819	1 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑥∀𝑦∀𝑧𝜓)

Syntax hints:   ↔ wb 206  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207

This theorem is referenced by:  dffun2  6571  dffun2OLD  6572  frpoins3xp3g  8166  xpord3inddlem  8179  cosscnvssid3  38477  dfeldisj3  38720