Theorem funALTVeqd 38667

Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013.)

Hypothesis

Ref	Expression
funALTVeqd.1	⊢ (𝜑 → 𝐴 = 𝐵)

Assertion

Ref	Expression
funALTVeqd	⊢ (𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))

Proof of Theorem funALTVeqd

Step	Hyp	Ref	Expression
1		funALTVeqd.1	. 2 ⊢ (𝜑 → 𝐴 = 𝐵)
2		funALTVeq 38665	. 2 ⊢ (𝐴 = 𝐵 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))
3	1, 2	syl 17	1 ⊢ (𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))

Syntax hints:   → wi 4   ↔ wb 206   = wceq 1540   FunALTV wfunALTV 38173

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701  ax-sep 5246  ax-nul 5256  ax-pr 5382

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ral 3045  df-rex 3054  df-rab 3403  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4293  df-if 4485  df-sn 4586  df-pr 4588  df-op 4592  df-br 5103  df-opab 5165  df-id 5526  df-xp 5637  df-rel 5638  df-cnv 5639  df-co 5640  df-dm 5641  df-rn 5642  df-res 5643  df-coss 38375  df-cnvrefrel 38491  df-funALTV 38647

This theorem is referenced by: (None)